Department of Mathematics

  • Math Research
  • Senior Project

Senior Project Marketplace

Senior Project (MATH 401) is designed to be a capstone experience for Math undergraduates, where the students engage in research activities guided by a faculty member. To enroll in MATH 401, you need to choose a project topic and get in touch with a faculty member. You can come up with your own project idea, or choose one from the list below. The list is by no means exhaustive but will give you an idea of what kind of research each researcher is working on.

Senior project ideas

Joe champion - math education, statistical modeling of math education achievement.

Learn about large-scale educational achievement data and techniques for predicting students’ math achievement. Involves data wrangling, intermediate coding in R or Python (mostly adapting existing code), and a focus on data visualization. Background in mathematics education and/or statistics preferred.

High School Mathematics Curriculum Development

For mathematics education students – modify and create Desmos Teacher activities to align with high school mathematics standards. Focus on data, modeling, and technology-assisted representations.

Middle School Mathematics Curriculum Development

Adapt activities from the Algebra through Visual Patterns curriculum for delivery in the Desmos Teacher Activities platform. Involves some testing with students and collaboration with math education researchers.

Other project ideas

Dig into the history of a K-12 math topic and write a paper / make a poster, create an original math video.

Contact info

Joe Champion Faculty Profile

Samuel Coskey - Set theory, logic, and combinatorics

Combinatorics and graph theory.

Learn something new in one of these areas that wasn’t covered in Math 189/287/387. Use a new book, book chapter, online notes, or published article as a resource. Present the motivation, examples, and results with a poster.

Algebra or analysis or geometry

Learn something new in one of these areas that wasn’t covered in Math 305/311/314/405/414. Use a new book, book chapter, online notes, or published article as a resource. Present the motivation, examples, and results with a poster.

Math education

Choose a topic in college-level mathematics to present at the middle or high school level. Create a detailed lesson plan.

I am open to exploring anything in pure mathematics (and applied mathematics if you can take the lead). The important thing is to find resources at the right level for you.

Contact Info

Jens Harlander - Topology and Algebra (Group Theory)

Topics in graph theory, topics concerning the topology of surfaces, topics in linear algebra over rings.

Jens Harlander Faculty Profile Page

Uwe Kaiser - Geometric and Algebraic Topology, Quantum Computing

Quantum computing algorithms.

This project asks you to have some programming experience. You work on a specific quantum algorithm. You study programming in Microsoft’s quantum computing kit, see, try out examples, and study properties of the algorithm. Basic linear algebra skills are necessary in order to understand how algorithms are implemented using circuits. The minimal expectation is a poster to be presented in the senior showcase.

Tangles and Electrical Networks

In 1993 Goldman and Kauffman interpreted the continued fraction of a tangle as a conductance of a corresponding network. This projects asks to search for further relations between electrical networks and invariants of links and tangles. The starting point is a paper of mine on band-operations on links leading to a formula similar to the one by Goldman/Kauffman. Basic linear algebra and some familiarity with discrete mathematics like graph theory are helpful, also knowledge of basic notions concerning electrical networks. The minimal expectation is a poster to be presented in the senior showcase.

Robotics and Topology

Topology and robotics are related through notion of configuration space. For example the configuration space of a robot arm in 3-space is a product of 2-spheres. Restrictions on motions lead to more interesting topology of configuration spaces. The goal is to study the complexity of basic examples through well-known theory developed by Farber. Knowledge of basic topology (for example MATH 411) is necessary for an understanding of the theory. The minimal expectation is a poster to be presented in the senior showcase.

Analysis Situs

In the years 1899 to 1904, Poincare published a paper with the title Analysis Situs and five supplements introducing basic ideas of topology. This project aims to study the way he introduced a particular concept, like e.g. the orientation of a manifold, and to research pre-Poincare origins of this concept (what was a building on?) and how the concept developed into modern times. The prerequisite for this project is the maturity of a senior, the willingness to read old mathematics literature (English translations are available). The expectation is a poster to be presented in the senior showcase.

[email protected]

Michal Kopera - Computational Math, Ocean Modeling

Broncorank - a new university ranking.

In this project, you will explore the idea of using a PageRank algorithm, which Google is using to rank websites in their search engine, for creating a university ranking which does not depend on some editorial board decision but emerges from each university peer institution lists. You will get a chance to work at an intersection of mathematics, programming, data science, and contribute to creating a more fair tool to rank universities across the U.S.

To be successful in this project, you need some background in programming and ideally have enjoyed your MATH 265 and/or 365 courses. Knowledge of basic linear algebra (matrices) is a plus. The minimum expectation is a poster presentation at Senior Showcase.

Ice/ocean interactions

The modeling of the interface between ice and the ocean is of utmost importance for climate science. You will experiment with models of ice/ocean boundary developed in my group and evaluate whether they produce physical results. No ocean science background is required, but you should be comfortable with writing simple code. The minimum expectation is a poster presentation at Senior Showcase.

Computational modeling using ODEs and PDEs

The bulk of my work is using computational methods to simulate phenomena described by ordinary or partial differential equations. I am open to your ideas on what you would like to model, and we can create a project based on your input.

You will likely need to be able to program in MATLAB, Python, Julia, or other languages.  Knowing something about ODEs and/or PDEs is welcome. I am also open to problems that yield themselves to Machine Learning. The minimum expectation is a poster presentation at Senior Showcase.

Game of Life, Fractals and self-similarity

You will explore some of the concepts outlined above and write code to implement them. The minimum expectation is a poster presentation at Senior Showcase.

Mathematical Art

You will work with genetic (or other nature-inspired) algorithms that try to generate art. You can either focus on optimization algorithms that try to reproduce existing images or aim to generate original art and try to measure its esthetics. The minimum expectation is a poster presentation at Senior Showcase.

Michal Kopera Faculty Profile Page

Zach Teitler - Algebra and Algebraic Geometry

My specialty is algebra. I can work with you on projects in algebra, graph theory, combinatorics, number theory, any other area of pure math, or any subject that you’re interested in within pure math, applied math, statistics, or math education.

I am available to work with students on undergraduate senior thesis projects. You can email me if you’re looking for a senior thesis advisor, but first, read about what you can expect if we work together and what project ideas we can work on together.

Barbara Zubik-Kowal - Applied mathematics

Difference equations and applications.

Difference equations arise naturally in real-world applications involving discrete sets or populations, or as approximations to continuum models in science and engineering. Mathematically, difference equations can be described as mathematical equalities involving the values of a function of a discrete variable. A recurrence relation such as the logistic map, relevant to population dynamics, or the sequence of Fibonacci numbers, are simple examples. Many difference equations can be solved analogously to how one solves ordinary differential equations. However, it is well-known that most difference equations depicting real-life phenomena cannot be solved in closed form and other methods are necessary to obtain qualitative or quantitative information about the desired solutions, including their stability properties. This senior project can go in a number of directions depending upon the interests of the student. The project may involve theoretical aspects, including theoretical derivations and proof-writing, or computations, including writing new codes or modifying existing ones.

Integro-differential equations and applications

Integro-differential equations are central to modelling numerous natural and industrial phenomena across physics, biology, medicine, engineering, and other fields. As an example in the field of epidemiology, integro-differential equations are frequently used in the mathematical modelling of epidemics, such as when the age-structure of the population is important in determining the dynamics of an epidemic. Integro-differential equations involve both integrals and derivatives of a function. As very few systems of integro-differential equations have a closed-form solution, a range of mathematical methods are often used to obtain qualitative information about the solutions of classes of problems involving integro-differential equations, and approximation techniques are often used to obtain quantitative information about the corresponding solutions given some initial data. In contrast to ordinary and partial differential equations, initial data for integro-differential equations is frequently provided on a whole interval, rather than a single initial point in time. This means more initial data is used to supplement systems of integro-differential equations. This senior project can go in a number of directions depending upon the interests of the student. The project may involve theoretical aspects, including theoretical derivations and proof-writing, or computations, including writing new codes or modifying existing ones.

Differential inequalities and applications

Mathematical models for a range of biological, physical or industrial phenomena may be grouped into general classes of systems of differential equations. Even if the underlying mathematical models may involve complexities that make it hard or impossible to solve by hand, it is frequently possible to extract useful qualitative information about its solutions. Such qualitative information frequently suffices to answer key questions about a solution’s behaviour. Examples are its long-term behavior, existence and uniqueness, convergence properties, and its upper and lower bounds, such as maximal and minimal solutions. These properties, in turn, help us derive information about not only one, but a whole family of mathematical models constituting a given class of differential equations. This senior project can go in a number of directions depending upon the interests of the student. The project may involve theoretical aspects, including theoretical derivations and proof-writing, or computations, including writing new codes or modifying existing ones.

Principles of approximation and applications

Smooth functions arise frequently in the mathematical modeling of numerous real-world phenomena in the sciences and engineering, including both natural and industrial processes. An example is the solution to a SIR model of susceptible, infectious, or recovered individuals in epidemiology, or solutions to mathematical models of tumor growth. It is well known, however, that solutions to most mathematical models depicting real-world phenomena cannot, in general, be expressed in closed form. It is, however, possible to make progress by making appropriate approximations to obtain an estimate of the desired solution. Such approximations involve discretizing the domain from a continuous interval to a finite subset of grid points, solving the discrete systems of equations, computing continuous extensions, or interpolations, and performing error analysis. There are many ways of doing this, but it is important to understand how to do it in a way that preserves certain desired properties, in order to ensure that the resulting approximate solutions that we are getting are indeed approximate solutions to the problem we started out with, rather than spurious output. This senior project can go in a number of directions depending upon the interests of the student. The project may involve theoretical aspects, including theoretical derivations and proof-writing, or computations, including writing new codes or modifying existing ones.

Barbara Zubik-Kowal Faculty Profile Page

Ideas for Capstone or Honors Projects in Mathematics The ideas listed below for honors projects may spark an idea for a project.  They will also give you some ideas about what certain faculty members are interested in. Students are also invited to offer their own ideas for projects based on their own reading, coursework, or perhaps based on earlier work (for example, in a summer REU).  In that case, you should feel free approach a faculty member who might be willing to work with you.  (Or contact Ron Freiwald for suggestions about whom to talk with.) Some of the ideas listed below are harder and some easier.  Some involve working on actual problems while others involve learning about a problem and why it's important or interesting.  In some cases, there may be an easier version (special case) of a problem that is more accessible. If one of the areas sounds interesting to you, contact the faculty member to discuss the topic and your background in more depth. Math majors with a special interest in sciences should also explore the ideas found on the webpages for Biology , Chemistry , Earth and Planetary Sciences , and Physics (click on the marker to "Research for Undergrads" in the left frame). If there are ideas that involve also work with mathematics there, we're certainly will to explore some sort of cooperative project with you. Professor Al Baernstein (Analysis) I can direct a project involving random walks or related stochastic processes .

Professor Renato Feres (Geometry)

Some of following problems are meant to introduce you to advanced but well-established topics in graduate level math, others are much more open ended and may lead to original results. Some are more "theoretical" while others invite you to do some computer exploration. A few are probably pie-in-the-sky problems that, to me at least, are amusing to contemplate. Whatever the case, I'd be happy to discuss any of them with you and suggest reading material for anything in this list  that strikes your fancy.
1) The kinematics of rolling . (Riemannian geometry/Non-holonomic mechanical systems) On a smooth stone, draw a curve beginning at a point p , and hold the stone over a flat table with p as the point of contact. Now roll the stone over the plane of the table so that at all times the point of contact lies on the curve, being careful not to allow the stone to slip or twist.  We may equally well think that we are rolling the plane of the table over the surface of the stone along the given curve. Mechanical systems with this type of motion are said to have "non-holonomic" constraints, and are common fare in mechanics textbooks. Now imagine a tangent vector to the plane at p . This rolling of the plane over the surface provides a way to transport v along the curve, keeping it tangent at all times. The resulting vector field over the curve is said to be a "parallel" vector field. Show that there is a unique way to carry out this parallel translation. (Find a differential equation that describes the parallel vector field and use some appropriate existence and uniqueness theorem.) Let c be a short path joining p and q , whose velocity vector field is parallel. Show that c is the shortest path contained in the surface that joins p and q . Whether or not you fully succeed, this mechanical idea will give you a concrete way of thinking about ideas in differential geometry that might seem a bit abstract at first, such as Levi-Civita connection, parallel translation, geodesics, etc. Also look for an engineering text on Robotic manipulators and explain why such non-holonomic mechanical systems are important in that area of engineering. I don't know of many places where these things are explained in a simple way. Perhaps Geometric Control Theory by Velimir Jurdjevic is a place to start.  In the engineering literature, "A mathematical introduction to Robotic Manipulation" is a particularly good reference. 2) Geometry in very high dimensions . (Convex geometry) Geometry in very high dimensions is full of surprises. Consider the following easy exercise as a warm-up. Let B(n,r ) represent the ball of radius r , centered at the origin, in Euclidian n- space. Show that for arbitrarily small positive numbers a and b , there is a big enough N such that (100 - a )% of the volume of B(n,r ) is contained in the shell B(n,r ) - B(n,r - b ) for all n > N. Here is a much more surprising fact that you might like to think about. Let S(n-1) denote the sphere of radius 1 in dimension n . (It is the boundary of B(n,1 ) .)  Let f be a continuous function from S(n-1) into the real line that does not increase distances, that is, | f(p) - f(q) | is not bigger than | p - q | for any two points p and q on the sphere. ( f is said to be a "1-Lipschitz" function.) Then there exists a number M such that, for all positive a, no matter how small, the set of points p in S(n-1) such that | f(p) - M | > a has volume smaller than exp( -na^2 / 2 ). In words, this means that, taking away a set with very small volume (if the dimension is very large), f is very nearly a constant function, equal to M . This is much more than a geometric curiosity. In fact, such concentration of volume phenomenon is at the heart of statistics, for example. To make the point, consider the following. Let S(n-1, n^0.5) be the sphere in n -space whose radius is the square root of n . Let f denote the orthogonal projection from the sphere to one of the n coordinate directions, which we agree to call the x -direction. Show that the part of the sphere that projects to an interval a < x < b has volume very nearly (when n is big) equal to the integral from a to b of the standard normal distribution. (This is easy to show if you use the central limit theorem). For a nice introduction to this whole subject, see the article by Keith M. Ball in the volume Flavors of Geometry , Cambridge University Press, Ed.: S. Levy, 1997. 3) Hodge theory and Electromagnetism . (Algebraic topology/Physics) Electromagnetic theory since the time of Maxwell has been an important source of new mathematics. This is particularly true for topology, specially for what is called "algebraic topology". One fundamental topic in algebraic topology with strong ties to electromagnetism is the so called "Hodge-de Rham theory".  Although in its general form this is a difficult and technical topic, it is possible to go a long way into the subject with only Math 233.  The article "Vector Calculus and the Topology of Domains in 3-Space", by Cantarella, DeTurck and Gluck (The American Mathematical Monthly, V. 109, N. 5, 409-442) is the ideal reference for a project in this area. (It has as well some inspiring pictures.) Another direction to explore is the theory of direct current electric circuits (remember Kirkhoff's laws?). In fact, an electric circuit may be regarded as electric and magnetic field over a region in 3-space that is very nearly one dimensional, typically with very complicated topology (a graph). Solving circuit problems implicitly involve the kind of algebraic topology related to Hodge theory.  (Hermann Weyl may have been the first to look into electric circuits from this point of view.) The simplification here is that the mathematics involved reduces to finite dimensional linear algebra. A nice reference for this is appendix B of The Geometry of Physics (T. Frankel), as well as " A Course in Mathematics for Students of Physics " vol. 2, by Bamberg and Sternberg. 4) Symmetries of differential equations . (Lie groups, Lie algebras/Differential equations) Most of the time spent in courses on ODEs, like Math 217, is devoted to linear differential equations, although a few examples of non-linear equations are also mentioned, only to be quickly dismissed as odd cases that cannot be approached by any general method for finding solutions. (One good and important example is the Riccati equation.)  It turns out that there is a powerful general method to analyze nonlinear equations that sometimes allows you to obtain explicit solutions. The method is based on looking first for all the (infinitesimal) symmetries of the differential equation. (A symmetry of a differential equation is a transformation that sends solutions to solutions. An infinitesimal symmetry is a vector field that generates a flow of symmetries.) The key point is that finding infinitesimal symmetries amounts to solving linear differential equations and may be a much easier problem than to solve the equation we started with. Use this idea to solve the Riccati equation. Choose your favorite non-linear differential equation and study its algebra of infinitesimal symmetries (a Lie algebra).  What kind of information do they provide about  the solutions of the equation? Since my description here is hopelessly vague, you might like to browse Symmetry Methods for Differential Equations - A Beginner's Guide by Peter Hydon, Cambridge University Press. It will give you a good idea of what this is all about. 5) Riemann surfaces and optical metric . (Riemannian geometry/Optics) Light propagates in a transparent medium with velocity c/n, where c is a constant and n is the so called "refractive index"  -- a quantity that can vary from point to point depending on the electric and magnetic properties of the medium. For a given curve in space, the time an imaginary particle would take to traverse its length, having at each point the same speed light would have there, is called the "optical length" of the curve.  Therefore, the optical length is the line integral of n/c along the curve with respect to the arc-length parameter. According to Fermat's principle, the actual path taken by a light ray in space locally minimizes the "optical length".  It is possible to use the optical length (for some given function n) to defined a new geometry whose geodesic curves are the paths taken by light rays.  This is a particular type  of Riemannian geometry, called "conformally" Euclidian. All this also makes sense in dimension 2. One of the most famous paintings of Escher show a disc filled with little angels and demons crowding towards the boundary circle. What refractive index would produce the metric distortions shown in that picture? A fundamental result about the geometry of surfaces states that, no matter what shape they have, you can always find a coordinate system in a neighborhood of any point that makes the surface conformally Euclidian. Why is this so? (This will require that you learn something about so called "isothermal coordinates".) 6) Random walks and diffusion limits (I) . (Probability theory/ElementaryGeometry) Imagine a long and narrow cylinder of radius r and a point particle that moves in the region bounded by the cylinder. The motion is specified as follows: starting at a point on the inner wall of the cylinder, choose at random a direction and let the particle move with constant speeduntil it hits another  point of the cylinder. Once there, choose a new direction at random  and repeat the process.  A  natural  scheme (for reasons I won't describe here)  is to pick the random direction with probability proportional to the cosine of the angle it makes with the (inward pointing) normal  vector.  The problem is to determine the probability that the particle will be given distance away from the initial point at a given time in the future.  It is actually hard to find such a probability explicitly, but if the cylinder is very narrow and the particle moves very fast (with speed proportional to the reciprocal of the radius) you can use the central limit theorem to obtain an explicit (Gaussian) approximation. What is the variance of the resulting normal law? How does the variance change if the cross section of the tube is, say a square, instead of a circle? 7) Random walks and diffusion limits (II) . (Probability theory) We can, of course, consider a two dimensional variant of the previous problem, in which the cylinder consists  of two infinite parallel lines and the particle  velocity after collision  is chosen according to the same cosine law. However, after some thought you will realize that the hypothesis of the  central limit  theorem fail (barely!) to hold. Nevertheless, we can still ask what kind of limit process this random walk leads to. (Some key words:   stable distributions, Levy processes.) 8) Random Billiards . (Billiard systems/Probability theory) You may have heard a lot about the  mathematical theory of chaos. It is part of the general subject of Dynamical Systems. In the tool box of the practitioners of this subject is a kind of toy system that is used to explore and illustrate almost any conceivable dynamical behavior (including chaos),  called "billiard systems". It is just what you might expect: a billiard table and a point mass that moves about and bounces off the sides according to the law of mirror reflection. But the table is allowed any shape you want. The problem I would like to propose is actually related to 6) and 7). Take the setting of RW2, except that the two parallel lines, when examined with strong lenses, reveal a periodic structure. More precisely, replace those lines with the graphs of, say, C sin( x / C ) and 1+ C sin( x / C ), where C is very small. Intuitively, as C approaches 0, the (deterministic) billiard system should behave more and more like the probabilistic system of 7). How can this intuition be made precise? What kind of scattering probability results after passing to the limit? What does the cosine law of 6) and 7), in particular, have to do with all this? 9) Existence of surfaces . (Computer Science/Differential Geometry) You've probably heard of cellular =automata. The most celebrated example among them is John Conway's "game of life". They are, in general, a sort of beads game played over an infinite lattice (grid),  which in our case will have dimension 3. At each moment, a lattice point  may be empty or occupied by a bead of one among a number of colors. At the next moment, the state of that lattice point is renewed according to some function of the state of the nearest neighbor points. This function specifies the rules of the game. Our problem is to find rules that will cause the beads to organize themselves into "surfaces". (Suggestion: try to find rules that imitate the behavior of amphiphilic molecules, like the lipid bilayers that make up biological membranes. These molecules have one end that "likes" water and another that "hates" it.)  If such surfaces can be obtained, is it possible to control how "crumpled" or "smooth" they are? or to control their curvature? Is it possible to make sense of notions such as differentiability and curvature in this discrete setting?  (This would  require the passage  to some appropriate scaling limit.) 10) Chemical varieties . (Algebraic geometry/Chemical kinetics) Algebraic geometry studies the geometry of sets of solutions of systems of polynomial equations (typically over the field of complex numbers) and how that geometry relates to the algebra of all polynomials  that vanish on the set. It is not difficult to show that to every system of chemical reactions with specified reaction speeds is associated a system of nonlinear first order differential equations describing how reactant concentrations change in time. These differential equations are of a very special kind: on the left-hand side is the first derivative of each reactant concentration (in moles) and on the right a polynomial function of the concentrations, whose coefficients are the stoechiometric constants. (Incidentally, the whole business of stoechiometry and its linear algebra underpinnings is in itself a great subject for a project.) The set of zeros of the polynomial equation are equilibrium concentrations for the chemical reactions. Call the set of complex solutions of the polynomial equations the "Chemical Variety" of the system of reactions. These should be very special algebraic varieties. (They are typically of degree 2, for example, for any reasonable reaction mechanism.)  Choose your favorite reaction mechanism and describe, in as much detail as you can, the geometric properties of the associated chemical variety. Are there interesting special properties shared by all chemical varieties?  

2)  Let U be a planar region, and let G be the group of rigid motions of the plane that map U to itself.   We call G the "automorphism group" of U , and we denote it by  Aut( U ).  Now suppose that  U'  is a small perturbation of U .  How is  Aut( U ' ), as a group, related to  Aut( U ) ?  How does the answer change as U '  deviates farther and farther from U ?

3)  ( Refer to (2) for terminology .)  Let G be any finite group.  Is there a planar domain U such that Aut( U ) = G ?  Can we relate the topology of U to the structure of the group?  What if we allow U to live in a higher dimensional space?  Does that allow more groups G to give an affirmative answer? Given a group G , can we estimate the dimension of the space in which a domain U will live that has the desired property?

4)  ( Refer to (2) for terminology .)  It is an intuitively obvious assertion that, of all planar domains, the disc has the "largest" automorphism group.  Formulate a precise version of this statement and prove it.  Given any group G   that is the automorphism group of some planar domain, can we find a particular planar domain U that is as close to the disc as we please and so that  Aut( U ) = G ?

5)  Consider the space C ^\infty  of infinitely differentiable functions and the space C ^\omega  of real analytic functions (i.e., functions with convergent power series expansions).  Of course  C ^\omega is a subset of C ^\infty.  Is there a range of function spaces, perhaps a range that is parametrized, that spans the gamut between  C ^\omega to  C ^\infty ?  ( This problem is important for the theory of partial differential equations .)

1) If a1,a2, are integers with gcd = 1, then the Eulidean algorithm implies that there exists a (n x n)-matrix A with integer entries, with first row = (a1,a2,...,an), and such that det(A) = 1.  A similar question was raised by J.P. Serre for polynomial rings over a field, with the a's being polynomials in several variables.  This fundamental question generated an enormous amount of mathematics (giving birth to some new fields) and was finally settled almost simultaneously by D. Quillen and A. A. Suslin, independently.  Now, there are fairly elementary proofs of this which require only some knowledge of polynomials and a good background in linear algebra.  This could be an excellent project for someone who wants to learn some important and interesting mathematics.  ( These results seem to be of great interest to people working in control theory.  Though I am not an expert, I'm willing to learn with a motivated student. 2) A basic question in number theory and theoretical computer science is to find a `nice' algorithm to decide whether a given number is prime or not. This has important applications in secure transmissions over the internet and techniques like RSA cryptosystems. Of course, the ancient method of Eratosthenes (sieve method) is one such algorithm, albeit a very inefficient one. All the methods availabe so far has been known to take exponential time. There are probabilistic methods to determine whether a number is prime, which take only polynomial time. The drawback is that there is a small chance of error in these methods. So, computer scientists have been trying for the last decade to find a deterministic algorithm which works in polynomial time. Recently, this has been achieved by three scientists from IIT, Kanpur, India. A copy of their article can be downloaded from A nice project would be to understand their arguments (which is very elementary and uses only a little bit of algebra and number theory) and may be to do a project on the history of the problem and its ramifications.   
1) ( Fluid Dynamics )  Consider a cylindrical tube, open at one end. At the closed end, a small quantity of gas is injected. It diffuses out the other end at a predictable rate. Now, suppose the quantity of gas injected is increased. The flow will not scale linearly, as the effect of the pressure of the introduced gas must be considered. I have a project with Professor Gregory Yablonksky in the Chemical Engineering department to model this flow. 2) ( Linear Matrix Inequalities ) A computer vision problem posed by Professor Robert Pless in the Computer Science Department. Imagine a large number of cameras arranged around a central object. One wants to match up the pictures, but there is some error in the measurement. Mathematically, the problem becomes approximating a large symmetric matrix by a rank 3 matrix that has 1's on the diagonal. It ties in to an active research area in systems theory: solving a linear matrix inequality with a rank constraint. Nobody knows how to do this well. 3) ( Applied Statistics/Public Health )  The "French paradox" is the claim that, despite having a high fat diet, French people have a low rate of heart disease. I believe this is a statistical artifact, due principally to cultural differences in filling out death certificates. I would be willing to supervise an undergraduate who wished to hunt down the data and analyze it.  
Mathematical population genetics : What determines the fate of a gene in a population? How can good genes go extinct? How fast are genes (good or bad) lost? How important are random forces? How good are the approximations? The methods that will be used are Markov processes in probability theory, diffusion processes in probability theory, scientific computing to analyze problems that are difficult to analyze theoretically, or a combination of these.  
1) Computation in topological combinatorics - Topological combinatorics includes the study of simplicial complexes (that is, geometric objects built from possibly higher dimensional analogues of the unit interval, the equilateral triangle and the equilateral tetrahedron) whose faces are indexed by combinatorial objects such as graphs.  The Homology program of J.-G. Dumas, F. Heckenbach, D. Saunders and V. Welker has been used to investigate the structure of such complexes.  There are many adjustments and additions which could be made to improve the program, the most ambitious of which is to make it amenable to parallel processing. 2) Order complexes of subgroup lattices - The set of subgroups of a group G is partially ordered by inclusion.  There are interesting open questions and proven theorems about relating the algebraic structure of G to the combinatorial structure of this partially ordered set.  For any partially ordered set P, the set of all totally ordered subsets of P determines a simplicial complex.  The topological structure of this complex is related to the combinatorial structure of P.  One can hope to use this relationship productively when P is the set of subgroups of G. This area is appropriate for both reseach and expository projects. 3) Symmetric functions - A symmetric function is a power series of bounded degree in infinitely many variables which is not changed by any permutation of the variables.  Symmetric functions appear in many areas of mathematics, including combinatorics and representation theory (which involves studying a group G by understanding homomorphisms from G to various matrix groups).  There are lots of interesting open combinatorial problems involving symmetric functions (many appear in the exercises after Chapter 7 of R. P. Stanley's book, Enumerative  Combinatorics, Volume 2).  This area is also appropriate for expository projects.
1) Read Daubechies and Sweldens "Factoring Wavelet Transforms into Lifting Steps," (J. Fourier Anal. Appl. 4:3(1998),245-267).  Then implement the Euclidean algorithm for Laurent polynomials described in the paper. ( Thus, you will use ideas in abstract algebra and Fourier analysis to write an efficient computer program that is part of the JPEG-2000 image compression algorithm. ) 2) Read chapter 3 (pp. 67-101) of my book "Adapted Wavelet Analysis," and also Strang, "The Discrete Cosine Transform" (SIAM Review 41:1(1999),135-147).  Synthesize a proof that the discrete Hartley transform is orthogonal. ( Thus, you will see how the Sturm-Liouville theorem from differential equations can save many tedious computations in the verification that a basis, such as one used in the JPEG (1990) image compression algorithm, is orthonormal .)

Professor Guido Weiss ( Analysis )  

A large number of undergraduate research projects can be obtained by studying various reproducing systems (of vectors or functions). Let us consider an example.

An orthonormal basis (in Euclidean space or, more generally, a Hilbert space) is such a "reproducing system" in the sense that an arbitrary vector, v , equals the linear combination obtained by multiplying the individual elements of the basis elements by their inner products with v and then summing the vectors obtained.  Many such bases can be constructed by selecting an appropriate vector (or function) in the space being considered and applying certain basic operations on this function (translations, dilations, and modulations, for example).  Wavelets are examples of such systems and their construction offers a wide variety of research projects.  

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Home > Student Work > Capstone Projects > Mathematics

Mathematics Capstone Projects

Theses/dissertations from 2023 2023.

An Exploratory Study on Methods for Interpolating and Extrapolating Baseball Win-Loss Percentage , Giselle Palacios

Queuing Theory in Theme Parks , Matthew J. Watters

Theses/Dissertations from 2021 2021

Integers and Polynomials with Integer Coefficients for High School Students , Gabriella Nowobilski

Statistics Education in the Middle Grades , Todd Matthew Fatka

Teacher and Student Perspectives of Online and Blended Learning , Alina M. Garcia

The Chinese Remainder Theorem , Carol S. Jackson

The Method of Archimedes: A Mechanical Approach for Calculating Areas and Volumes , Patricia Esparza

Theses/Dissertations from 2019 2019

Modelling Illinois Community College Online Enrollments versus the Economy from 2008-2018 , John D. Jennings

Optimization of Mathematical Functions Using Gradient Descent Based Algorithms , Hala Elashmawi

The Evolution of the AP Calculus AB Test: 1955-2018 , Scott Bennett

Theses/Dissertations from 2018 2018

Connecting High School Mathematics and Abstract Algebra , Abbey Scupin

Methodologies of Financial Data Management and Analysis , Luke Dauparas

The Role of Sophie Germain in Solving Fermat's Last Theorem , Amal Yaqoub Yosef

Theses/Dissertations from 2017 2017

An Introduction to the Lebesgue Integral , Ikhlas Adi

Assessment Literacy in a Mathematics Classroom , Virginia M. Doran

Fitting a Linear Regression Model and Forecasting in R in the Presence of Heteroskedascity with Particular Reference to Advanced Regression Technique Dataset on , Samuel Mbah Nde

International Baccalaureate Mathematics, Advanced Placement Mathematics, and Dual Credit Mathematics Courses – An In Depth Look , Lawrence Benjamin Jaskunas

Strategies for Overcoming Math Anxiety in Developmental Math Students at Community Colleges , Nika Alex

The Necessity of Fundamental Math in College , Spencer A. McDuffy, Sr.

The Transition from ACT to SAT as the Illinois College Entrance Exam and the Potential Implications on Student Scores in Mathematics , William Rose

Transfinite Ordinal Arithmetic , James Roger Clark

Capstones from 2016 2016

Algebra Tutorial for Prospective Calculus Students , Matthew McKain

A Little Aspect of Real Analysis, Topology and Probability , Asmaa A. Abdulhameed

History of Mathematics from the Islamic World , Asamah Abdallah

Nested Monte Carlo Tree Search as Applied to Samurai Sudoku , Laura Finley

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Student work

Leilani Leslie Mathematical Framework for Teaching: A Lesson Analysis Faculty Sponsor: Sarah Hanusch

Abstract: Researcher and mathematics educator Deborah Loewenberg Ball has spent over 30 years researching effective practices for teaching mathematics. Her research is an expansion of research done by educational psychologist Lee S. Shulman (1896) on teacher knowledge.

Deborah Ball’s cumulative research efforts resulted in what she calls Mathematical Knowledge for Teaching. Mathematical Knowledge for Teaching “encompasses abilities such as analyzing the student thinking that led to an incorrect answer, identifying the mathematical understanding a student does not yet have, and deciding how to best represent a mathematical idea so that it can be understood by students” (Chapman, 2017). In other words, Mathematical Knowledge for Teaching acknowledges that math teachers need to be dually equipped with subject matter knowledge and pedagogical content knowledge for the most effective delivery of content (Ball, Thames & Phelps, 2008, p. 391). Ball classified both, subject matter knowledge and pedagogical content knowledge, into 3 distinct subdomains, respectively. This capstone paper will thoroughly define each of those subdomains. After defining each subdomain I will take a math lesson that I have taught and analyze it through the lenses of the Mathematical Knowledge for Teaching framework.

Nathan Caldwell Quandles and Alexander Polynomials in Knot Theory Faculty Sponsor: Rasika Churchill

David Cleverley Ideals of Varieties of Five Points Faculty Sponsor: John Myers

Abstract:  Let V = {p_1, · · · , p_k} be a finite set of points in P^2. Then, it is a general fact that there is a finite set S of polynomials with the following properties: every point in V lies on an intersection of all of the curves and all of the curves’ intersection points are in V . There exist many such sets fulfilling those conditions, but this paper is particularly interested in finding the one with the least amount of elements, given a set V with five points all on a line or else. The main result is that, if the five points lie on the same line, only two polynomials are needed to form an intersection of just those points. Further, when the points are not all on a line, it can be constructively shown that only three polynomials are needed to form the intersection, provided the points lie in a plane over an infinite field.

Jeremy Brandel Study of Students Working with White Boards Faculty Sponsor: Preety Tripathi

Kati Barney Chemometrics with R Faculty Sponsor: Mark Baker Karl Mosbo Lebesgue Integration Faculty Sponsor: Mark Elmer

Abstract:  In the spring of 2020, I studied measure theory under professor Mark Elmer’s advisement. I read and did problems from ”A User-friendly Introduction to Lebesgue Measure and Integration” by Gail S. Nelson. We reviewed Riemann integration, then studied outer measure, Lebesgue measure, measurable functions, and finally Lebesgue integration.

This paper will review the concept of Lebesgue measure and Lebesgue integration as presented by Nelson, followed by my proposing a different way of setting up Lebesgue integration while simultaneously being equivalent. Nicole Wightman Level Progression of Proof Writing Faculty Sponsor: Jeff Slye Nicolas van Kempen On separating systems and covers Faculty Sponsor: Greg Churchill

Abstract:  Separating systems and covers deal with both graph theory and combinatorics. Taking an n-element vertex set V , we will present what is means for a pair A and B of subsets of V to separate two given vertices, and extend that definition to a family of such pairs, separating any two vertices of V , creating what we call a separating system. We will consider two optimization problems related to separating systems, first trying to minimize the number of pairs of subsets in our separating system, and then examining a weighted version, minimizing the total number of vertices in the separating system. We will then show a technique that can be used to build an optimal separating system with regards to both problems. Finally, we will extend these concepts to hypergraphs and covers, and discuss a connection between the problems of finding an optimal cover and finding a family of perfect hash functions. Juliann Geraci Constructions of free resolutions through simplicial complexes Faculty Sponsor: John Myers

Abstract:  From a simplicial complex ∆ we can build a chain complex C(∆) which gives an algebraic encoding of information about ∆. We will recognize a fundamental connection between simplicial complexes and commutative algebra through C(∆), which enables us to understand a result of Bayer, Peeva, and Sturmfels that gives an effective way to describe some resolutions in terms of labeled simplicial complexes. Brett Meerdink: Approximate and Exact Solutions to the Motion of a Simple Pendulum Faculty Sponsor: Zheng Hao

Abstract:  The simple pendulum is one of the most studied cases of non-linear motion. At small angles its motion appears linear, however, is non-linear at large angles. This caused by the simple pendulum’s differential equation having a non-linear term (sine of the angle). This term can be approximated using the small angle approximation which linearizes the differential equation resulting in a linear solution. This solution is accurate at describing a simple pendulum’s motion at small angles but fails at large angles, which is described by Jacobian elliptic functions. Approximate solutions for the motion of a pendulum have been developed to describe a simple pendulum’s motion at large angles. Three such approximations are were developed in Bel ́endez, A. et al., Borghi R. et al., and Johannessen, K. et al using an ansatz, Fourier series and homotropy perturbation method respectively. These methods may be used to describe the motion of a pendulum at large angles and converge for smaller angles with the exact and small angle approximation solutions.

Sam Morley Empirical and Theoretical Probability and the Most Underrated Player in NBA History Faculty Sponsor: Greg Churchill

Abstract:  In my final semester here at SUNY Oswego, I worked with Dr. Gregory Churchill contemplating what I will call the triple-double problem, an exercise in empirical as well as theoretical probability. That is, what is the probability that an NBA player will acheive double-digit averages in points, rebounds, and assists over the course of an NBA season. With our findings I develop an argument for why Oscar Robinson is the most underrated player in NBA history.

Kendra Walker Fibonacci numbers and coin tossing distributions Faculty Sponsors: Ampalavanar Nanthakumar, Magdalena Mosbo

Abstract:  A scenario in which an unbiased coin is tossed until two consecutive heads are achieved results in a probability distribution containing Fibonacci numbers in its numerator. The probability for a sequence of n spaces and with specific place holders, called strings, of heads and tails patterns will be derived. Also, formulas to explicitly and mathematically provide reasoning for the appearance of the Fibonacci numbers will be investigated, even extending the scenario to three consecutive heads to look for patterns. Exploring the expected value, variance, skewness, kurtosis, and moment generating functions for both the two consecutive heads scenario and the three consecutive heads scenario will give insight on the distributions’ characteristics.

We find that this situation applies to four and five heads and then extends to n consecutive head scenarios as well. We will use an R program to confirm the statistical properties derived from each coin tossing scenario and also provide a basis to look at how further “n-acci” sequences compare to our two and three consecutive head scenarios.

Casey Stone A primal-dual method to solving the obstacle problem
 Faculty Sponsor: Zheng Hao Abstract:  This semester I worked with Dr. Zheng Hao studying the obstacle problem. Throughout the semester I studied a numeric method to solve this problem and explored a solution to the obstacle problem using the Primal-Dual Method and MATLAB code to run this algorithm. I then compared the work Junwei Lu did on approximating the 2D obstacle problem with the Finite Difference Method, under the advisement of Dr. Hao, with my work on the 2D obstacle problem.

Andrew Smith Cubic spline interpolation
 Faculty Sponsor: Elizabeth Wilcox Abstract:  A cubic spline is a piecewise smooth cubic polynomial that interpolates a set of ordered data points. Cubic spline interpolation is often chosen over polynomial interpolation because of better behavior controls and often less computational overhead. While cubic spline interpolation is often viewed as a way to interpolate data points, it can also be used to model the curve of natural or man-made objects. This was the premise of Roel J. Stroeker’s paper “On the Shape of a Violin,” in which Stroker derived a cubic spline to describe the shape of a violin, which could then be made.[3] Likewise, other interpolation methods such as thin plate spline interpolation appear to be useful modeling tools for real life objects, as seen in fields such as morphometrics. The purpose of this project though was to learn about cubic spline interpolation, and write a program that could model real world inputs, and produce graphics to potentially fabricate a model.

Colin Beshures On the Hilbert series of a graded ring Faculty Sponsor: John Myers Abstract:  In this paper we will compute the dimension (or size) of rings. For this, we split a ring into an infinite sequence of vector spaces, which yields an infinite sequence of dimensions. We then use the growth of this sequence as the dimension of the ring. We quantify this growth using objects called Hilbert series, and our main tool to compute Hilbert series is an advanced form of linear algebra.

Elizabeth Andrews Julia Robinson and the J.R. Hypothesis Faculty Sponsor: Sarah Hanusch Abstract:  Julia Robinson is one of the most renowned mathematicians of the twentieth century. The first woman elected president of the National Academy of Sciences, Robinson’s career in mathematics spanned over thirty years. Her love for both number theory and recursion as a young college student led her to study Hilbert’s tenth problem, commencing her life’s work. It is her conjecture, namely the J.R. Hypothesis, that ultimately led to the groundbreaking solution to Hilbert’s tenth problem, proving her invaluable to the math community. In this paper, I will discuss not only her personal life, but I will also expound upon her famous hypothesis, discussing the key terms and theorems in her work.

Junwei Lu A Finite Difference Method Approach to Numerical Solutions to Obstacle Problem with Constant Boundary Values
 Faculty Sponsor: Zheng Hao Abstract:  This paper is description of the Obstacle problem. The obstacle problem is one of the main motivations for the development of the theory of variational inequalities and the problematic of free boundary problems.

Olivia Peel Investigation of the Distribution of the Collison Data Faculty Sponsor: Ampalavanar Nanthakumar Abstract:  This project aims to study the probability distributions that are involved in analyzing collision related data. The monthly data collected over a period of three years by a local body shop was used in this study. The data showed that the amount of collisions related damages is normally distributed while the number of parts needed to repair these vehicles (which is nested within the number of damaged vehicles) is Poisson distributed. Goodness-of-fit tests were performed to confirm the distributional patterns.

Kamani Marchant & Kevon Cambridge Joint distribution of Directional Data Faculty Sponsor: Ampalavanar Nanthakumar Abstract:  The directional data is very common in meteorology, spatial modeling, geology, dentistry etc. For example, wind speed and wind direction form a bivariate directional data. The project considered the descriptive and inferential aspects of bivariate directional data.

Darryl Gomes-Lewis NCAA Probability Analysis Faculty Sponsor: Ampalavanar Nanthakumar Abstract:  The project deals with a probability analysis to see whether a low ranked team could beat a top seeded team in the NCAA basketball tournaments.

Lennisha John A Study of Benford’s Law Faculty Sponsor: Ampalavanar Nanthakumar Abstract:  The project aims to verify the Benford’s Law empirically by looking at some published numerical tables.

Jonathan Edwards Euro Jackpot Lottery Faculty Sponsor: Ampalavanar Nanthakumar Abstract:  The project uses a probabilistic analysis to study the pattern of winning lottery numbers in European Jackpot Lotteries.

Victoria Nguyen Regular Calculus vs Stochastic Calculus Faculty Sponsor: Ampalavanar Nanthakumar Abstract:  The project was on explaining the similarities and dissimilarities between the regular Calculus and the Stochastic Calculus. Some examples were given to show the differences.

Erika Wilson Investigation of Cepheid Period-Luminosity Relationship Faculty Sponsor: A. Nanthakumar Abstract:  This research encompasses the use of many statistical software programs to fit four different copula models on data that measures the Cepheid Period-Luminosity Relation. We first discuss basic copula theory and its applications. Next, we talk about the techniques of data classification used and the results from this procedure. We then move on to fitting copula models and how to do so. We conclude with a discussion of how we analyzed and proved a suspected break in data at the point of X=1.

Kyle Buscaglia & Sean Crowder Hidden Markov Chain in Ice-hockey Faculty Sponsor: A. Nanthakumar Abstract:  This research focuses at how the concept of Markov Chains and Hidden Markov Chains can be applied in analyzing Ice-hockey games from the videos.

Laura Murtha Building a Foundation for Calculus Faculty Sponsor: Terry Tiballi Abstract:  It took approximately 100 years from the development of calculus for it to become rigorous and logically sound. Unfortunately, a majority of the calculus students never see the rigor behind it. I will take several facts of calculus that are taken for granted and prove they are logically sound through real analysis. I will walk through a set of problems from the book Real Analysis: A First Course by Russell A. Gordon to shed light on the underlying connections in the proof of major calculus facts and theorems.

Nicholas Powers The Use of Mathematics in Nuclear Physics Faculty Sponsor: Sue Fettes Abstract:  Problems in nuclear physics will be discussed and examined from a mathematical standpoint. Specific examples will be looked at in which nuclear physics problems are solved using algebra and calculus. The derivation of certain equations used in nuclear physics will also be briefly examined.

Jacob Gallagher Linear Fractional Transformations in the Complex Plane Faculty Sponsor: Terry Tiballi Abstract:  I will be talking about what a linear fractional transformation is and the different situations that might arise. I will being giving a few simple examples of some of these situations. Then I will talk about a special case of linear fractional transformation with why and how circles are mapped to circles.

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geometry capstone project ideas

Capstone Projects for High School Students

Padya Paramita

February 10, 2020

geometry capstone project ideas

As colleges get more and more selective, you might be worried about how you can stand out among the thousands of talented candidates. One useful tip to keep in mind is that admissions officers want students who are truly passionate about what they do and have gone above and beyond to demonstrate their interests. If you’ve got an academic subject, topic, or even hobby that you love, consider taking on one of the many possible capstone projects for high school students . 

It’s never too early to start brainstorming, especially when considering broad fields such as biology and economics. Finding a specific topic that relates to you personally is especially important with interests such as writing and art that are common for many applicants. To guide you through the process, I have outlined what exactly is meant by capstone projects for high school students , provided some topic suggestions to give you an idea of what yours might look like, and finally, outlined how your project can benefit your chances in the college admissions process. 

What is a Capstone Project?

Capstone projects for high school students can take many different forms, depending on the topics that resonate with you, and what is feasible based on your location and the time you’re willing to spend. If you’d like a more concrete way to convey your skills, effort, and knowledge in a certain discipline, carrying out a capstone project - usually finished at the end of the school year - would be an effective way to reflect your interest. Throughout the project, you should make a plan, conduct research, maintain a portfolio if applicable, keep track of your progress, and finally, present it.

Students usually carry out these projects individually, but sometimes, depending on the breadth of the topic, form a group. You might want to find a mentor as a resource, though it’s not required. Choose a mentor who offers expertise in the field. For example, your history teacher can assist you on a paper about World War II, while your English teacher should be your go-to if you’re working on a poetry collection.

Once your project is ready, you should present your hard work in a form that makes sense for the field of your choice. Capstone projects for high school students could come to life in the form of a paper, video, public presentation, or something even more specific such as an app or book. You might submit it to a panel of your teachers or supervisors for a grade if applicable.

Brainstorming Topics for Capstone Projects for High School Students

Brainstorming capstone projects for high school students can be difficult. Where do you even start? Narrow down topics based on your intended major, career interest, or a problem in your community you’d want to tackle. You could even find an academic approach to one of your favorite extracurricular activities!

The project can take many forms. If you’re interested in studying filmmaking, you could create a short movie or documentary. If you’re conducting biological research, you could write an academic paper and try to get it published. Check out the following table, which we’ve divided up by fields, in order to inspire ideas for your own initiative as you continue brainstorming capstone projects for high school students . 

As you can see, there is a world of possibilities. Your projects can also be on a relatively small scale if you don’t have the resources or the time. If you have multiple interests, you can combine various fields, such as art and business, engineering and biology, writing and social justice. If you’re thinking about pursuing one of these capstone projects for high school students , carefully consider what you can genuinely put the most effort into and create something that is unique to you!

How Can a Capstone Project Help You in the Admissions Process?

You might be wondering whether conducting capstone projects for high school students helps with your college applications. If done well, such work can impress admissions officers, as it would show that you aren’t afraid of taking initiative. If you work on the project with a team, this could be a great demonstration of your leadership and collaboration skills. Over the course of your work, depending on your project, you can also hone your research, writing, and public speaking skills. 

Colleges appreciate students who are specialized in one or two particular areas. Starting your own capstone project can effectively emphasize your passion for your major or prospective career. Considering that you will probably work very hard on the project and that it might end up having a deep impact on you (and vice versa), you could find yourself writing your personal statement or supplemental essays on the experience. Having worked on a project like this would portray clear ambition on your part. Admissions officers would get a strong impression of the ways you would contribute to the campus community. 

At the end of the day, the sole purpose of your project shouldn’t be just to boost your application profile. Genuinely work hard on your project and make sure your reasons behind pursuing it are convincing. Admissions officers will organically get a sense of your intellectual pursuits and commitment to creating something beyond what’s expected out of your academic interests. 

Capstone projects for high school students not only convey your passion towards a field, but they help you develop and hone skills that can benefit you throughout the rest of your life. Remember, that taking on such a project requires time, dedication, and patience, so don’t tackle something huge unless you can handle it. But if you commit to it with enthusiasm and determination, your efforts can go a long way toward increasing your knowledge, impressing colleges, and positively contributing to your community. Good luck!

Tags : applying to college , capstone projects for high school students , what is a capstone project , excelling in high school , projects in high school

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The Best 150 Capstone Project Topic Ideas

10 May 2022

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❔What is a Capstone Project?

Capstone Project Ideas:

  • 💾Computer Science
  • 🎒High School Education
  • 💻Information Technology
  • 🎭Psychology
  • 🪄Management
  • 🪛Engineering
  • 💰Accounting

✅Capstone Writing: 10 Steps

The long path of research works ahead, and you can’t find any capstone project ideas that would be interesting and innovative? The task can seem even more challenging for you to feel all the responsibility of this first step. The top 150 capstone ideas presented below aim to make a choice not so effort-consuming.

With the list of the capstone project topics we've picked for you, you'll be covered in major subjects. Continue reading, and you'll get ideas for capstone projects in information technology, nursing, psychology, marketing, management, and more.

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What is a Capstone Project?

Educational institutions use the capstone project to evaluate your understanding of the course on various parameters. For the students, the work on the project gives an excellent opportunity to demonstrate their presentation, problem-solving and soft skills. Capstone projects are normally used in the curriculum of colleges and schools. Also called a senior exhibition or a culminating project, these assignments are given to finish the academic course.

This assignment has several different objectives, among which are the following:

  • to encourage independent planning,
  • to learn to meet up deadlines,
  • to practice a detailed analysis,
  • to work in teams.

It's not that easy to pick the right capstone paper topic. The problem intensifies as each student or separate teams have to work on a single assignment which has to be unique. The best capstone project ideas may possibly run out. However, whatever topic you opt for, you’d better start your preparation and research on the subject as early as possible.

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Amazing Capstone Project Ideas for Nursing Course

Studying nursing is challenging, as it requires a prominent theoretical foundation and is fully practical at the same time. You should have to do thorough research and provide evidence for your ideas, but what to start with? The preparation for your capstone project in nursing won’t be so overwhelming if you make use of these capstone title ideas:

  • Innovation and Improvement in Nursing
  • Vaccination Chart Creation
  • The Role of Nurses in Today's Society
  • Shortage in Nursing and Its Effects on Healthcare
  • Evidential Practices and Their Promotion in Nursing
  • Global Changes in the Approach to Vaccination
  • Top Emergency Practices
  • Preventive Interventions for ADHD
  • Quality of Nursing and Hospital Personnel Shifts: The Interrelation
  • Ways to Prevent Sexually Transmitted Diseases
  • Brand New Approaches in Diagnostics in the Nursing Field
  • Diabetes Mellitus in Young Adults: Prevention and Treatment
  • Healthcare in Ambulances: Methods of Improvement
  • Postpartum Depression Therapy
  • The Ways to Carry a Healthy Baby

Attractive Computer Science Capstone Project Ideas

Computer science is so rapidly developing that you might easily get lost in the new trends in the sphere. Gaming and internet security, machine learning and computer forensics, artificial intelligence, and database development – you first have to settle down on something. Check the topics for the capstone project examples below to pick one. Decide how deeply you will research the topic and define how wide or narrow the sphere of your investigation will be.

  • Cybersecurity: Threats and Elimination Ways
  • Data Mining in Commerce: Its Role and Perspectives
  • Programming Languages Evolution
  • Social Media Usage: How Safe It Is?
  • Classification of Images
  • Implementation of Artificial Intelligence in Insurance Cost Prediction
  • Key Security Concerns of Internet Banking
  • SaaS Technologies of the Modern Time
  • Evolvement of Mobile Gaming and Mobile Gambling
  • The Role of Cloud Computing and IoT in Modern Times
  • Chatbots and Their Role in Modern Customer Support
  • Computer Learning Hits and Misses
  • Digitalization of Education
  • Artificial Intelligence in Education: Perspectives
  • Software Quality Control: Top Modern Practices

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Several High School Education Capstone Project Ideas for Inspiration

High school education is a transit point in professional education and the most valuable period for personal soft skills development. No wonder that the list of capstone project ideas in high school education involves rather various topics. They may range from local startup analysis and engineer’s career path to bullying problems. It’s up to you to use the chosen statement as the ready capstone project title or just an idea for future development.

  • A Small Enterprise Business Plan
  • Advantages and Disadvantages of Virtual Learning in Schools
  • Space Tourism: The Start and Development
  • Pros and Cons of Uniforms and Dress Codes
  • What is Cyberbullying and How to Reduce It
  • Becoming a Doctor: Find Your Way
  • Career in Sports: Pros and Cons
  • How to Eliminate the Risks of Peer Pressure
  • Ensuring Better Behaviours in Classroom
  • Cutting-Edge Technologies: NASA versus SpaceX
  • The Reverse Side of Shyness
  • Stress in High School and the Ways to Minimize It
  • How to Bring Up a Leader
  • Outdated Education Practices
  • Learning Disabilities: What to Pay Attention to in Children’s Development

Capstone Project Topics in Information Technology – Search for Your Best

Information technology is a separate area developed on the basis of computer science, and it might be challenging to capture the differences between them. If you hesitate about what to start with – use the following topics for capstone project as the starting point for your capstone research topics.

  • Types of Databases in Information Systems
  • Voice Recognition Technology and Its Benefits
  • The Perspectives of Cloud Computing
  • Security Issues of VPN Usage
  • Censorship in Internet Worldwide
  • Problems of Safe and Secure Internet Environment
  • The Cryptocurrency Market: What Are the Development Paths?
  • Analytics in the Oil and Gas Industry: The Benefits of Big Data Utilization
  • Procedures, Strengths and Weaknesses in Data Mining
  • Networking Protocols: Safety Evaluation
  • Implementation of Smart Systems in Parking
  • Workplace Agile Methodology
  • Manual Testing vs. Automated Testing
  • Programming Algorithms and the Differences Between Them
  • Strengths and Weaknesses of Cybersecurity

Psychology Capstone Project Ideas

Society shows increasing attention to mental health. The range of issues that influence human psychology is vast, and the choice may be difficult. You’ll find simple capstone project ideas to settle on in the following list.

  • The Impact of Abortion on Mental Health
  • Bipolar Disorder and Its Overall Effects on the Life Quality
  • How Gender Influences Depression
  • Inherited and Environmental Effects on Hyperactive Children
  • The Impact of Culture on Psychology
  • How Sleep Quality Influences the Work Performance
  • Long- and Short-Term Memory: The Comparison
  • Studying Schizophrenia
  • Terrorist’s Psychology: Comprehension and Treatment
  • The Reasons for Suicidal Behaviour
  • Aggression in Movies and Games and Its Effects on Teenagers
  • Military Psychology: Its Methods and Outcomes
  • The Reasons for Criminal Behavior: A Psychology Perspective
  • Psychological Assessment of Juvenile Sex Offenders
  • Do Colours Affect The Brain?

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Capstone Project Ideas for Management Course

Studying management means dealing with the most varied spheres of life, problem-solving in different business areas, and evaluating risks. The challenge starts when you select the appropriate topic for your capstone project. Let the following list help you come up with your ideas.

  • Innovative Approaches in Management in Different Industries
  • Analyzing Hotels Customer Service
  • Project Manager: Profile Evaluation
  • Crisis Management in Small Business Enterprises
  • Interrelation Between Corporate Strategies and Their Capital Structures
  • How to Develop an Efficient Corporate Strategy
  • The Reasons For Under-Representation of Managing Women
  • Ways to Create a Powerful Public Relations Strategy
  • The Increasing Role of Technology in Management
  • Fresh Trends in E-Commerce Management
  • Political Campaigns Project Management
  • The Risk Management Importance
  • Key Principles in the Management of Supply Chains
  • Relations with Suppliers in Business Management
  • Business Management: Globalization Impact

Capstone Project Ideas for Your Marketing Course

Marketing aims to make the business attractive to the customer and client-oriented. The variety of easy capstone project ideas below gives you the start for your research work.

  • How to Maximize Customer Engagement
  • Real Businesses Top Content Strategies
  • Creation of Brand Awareness in Online Environments
  • The Efficiency of Blogs in Traffic Generation
  • Marketing Strategies in B2B and B2C
  • Marketing and Globalization
  • Traditional Marketing and Online Marketing: Distinguishing Features
  • How Loyalty Programs Influence Customers
  • The Principles of E-Commerce Marketing
  • Brand Value Building Strategies
  • Personnel Metrics in Marketing
  • Social Media as Marketing Tools
  • Advertising Campaigns: The Importance of Jingles
  • How to Improve Marketing Channels
  • Habitual Buying Behaviours of Customers

Best Capstone Engineering Project Ideas

It’s difficult to find a more varied discipline than engineering. If you study it – you already know your specialization and occupational interest, but the list of ideas below can be helpful.

  • How to Make a Self-Flying Robot
  • How to Make Robotic Arm
  • Biomass Fuelled Water Heater
  • Geological Data: Transmission and Storage
  • Uphill Wheelchairs: The Use and Development
  • Types of Pollution Monitoring Systems
  • Operation Principles of Solar Panels
  • Developing a Playground for Children with Disabilities
  • The Car with a Remote-Control
  • Self-Driving Cars: Future or Fantasy?
  • The Perspectives of Stair-Climbing Wheelchair
  • Mechanisms of Motorized Chains
  • How to Build a Car Engine
  • Electric Vehicles are Environment-Friendly: Myth or Reality?
  • The Use of Engineering Advancements in Agriculture

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Capstone Project Ideas for MBA

Here you might read some senior capstone project ideas to help you with your MBA assignment.

  • Management Strategies for Developing Countries Businesses
  • New App Market Analysis
  • Corporate Downsizing and the Following Re-Organization
  • How to Make a Business Plan for a Start-Up
  • Relationships with Stakeholders
  • Small Teams: Culture and Conflict
  • Organization Managing Diversity
  • What to Pay Attention to in Business Outsourcing
  • Business Management and Globalization
  • The Most Recent HR Management Principles
  • Dealing with Conflicts in Large Companies
  • Culturally Differentiated Approaches in Management
  • Ethical Principles in Top-Tier Management
  • Corporate Strategy Design
  • Risk Management and Large Businesses

Capstone Project Ideas for an Accounting Course

Try these ideas for your Capstone Project in Accounting – and get the best result possible.

  • How Popular Accounting Theories Developed
  • Fixed Assets Accounting System
  • Accounting Principles in Information Systems
  • Interrelation Between Accounting and Ethical Decision-Making
  • Ways to Minimize a Company’s Tax Liabilities
  • Tax Evasion and Accounting: Key Principles
  • Auditing Firm Accounting Procedures
  • A New Accounting Theory Development
  • Accounting Software
  • Top Three World Recessions
  • Accounting Methods in Proprietorship
  • Accounting Standards Globally and Locally
  • Personal Finance and the Recession Effect
  • Company Accounting: Managerial Principles and Functions
  • Payroll Management Systems

Capstone Writing: 10 Essential Steps

Be it a senior capstone project of a high school pupil or the one for college, you follow these ten steps. This will ensure you’ll create a powerful capstone paper in the outcome and get the best grade:

  • One of the tips to choose a topic that your professors would be interested in is picking a subject in the course of your classes. Make notes during the term and you will definitely encounter an appropriate topic.
  • Opt for a precise topic rather than a general one. This concerns especially business subjects.
  • Have your capstone project topic approved by your professor.
  • Conduct a thorough information search before developing a structure.
  • Don’t hesitate to do surveys; they can provide extra points.
  • Schedule your time correctly, ensuring a large enough time gap for unpredictable needs.
  • Never avoid proofreading – this is the last but not least step before submission.
  • Stick up to the topic and logical structure of your work.
  • Get prepared to present your project to the audience, learn all the essential points, and stay confident.
  • Accept feedback open-mindedly from your teacher as well as your peers.

Preparation of a powerful capstone project involves both selection of an exciting topic and its in-depth examination. If you are interested in the topic, you'll be able to demonstrate to your professor a deep insight into the subject. The lists of ideas above will inspire you and prepare you for the successful completion of your project. Don’t hesitate to try them now!

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Daniel Howard

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What is a capstone project ? We have the whole blog dedicated to this question. Now, let's speak about worthy capstone project ideas as it is quite difficult to find them. You should use your research advisor’s help. Expert advice will help on the topic that will demonstrate what subject can be great for students’ proper training. You can overcome challenges and achieve required results by studying the topic thoroughly and understanding its essence. Use special academic articles, if you need help drawing a final line under the learning process. By choosing the main topic, you can reveal your skills and talents to the academic community, so no way should you neglect the preparation. You can get a good grade and demonstrate your best qualities by writing a single paper.

How to Come Up With Capstone Project Ideas

It takes time to look for the right capstone research project ideas. More so, than preparing the final paper. The fact is that it will be impossible to create an interesting project without having certain creative skills. Lacking ideas or insufficient work on covering your point will result in failure. Preparation for writing your capstone project includes this stages:

  • Study the existing topics that have been covered in other papers.
  • Contact your research advisor for help.
  • Search for interesting topics on the Internet.

You can study only if you focus on the relevant topic. The lacking interest is quite noticeable in the paper, which is unacceptable. By brainstorming before writing the project, you should discover your advantages and demonstrate them properly. If you want instant results, then check out our  capstone project writing service . 

Medical Capstone Project Ideas

The best capstone project medical ideas are developed following a sample, with a suitable direction being easy to find. Delivering high-quality performance of the paper is important. After all, your work result depends on it. Every interested graduate can find a worthy topic on the Internet. Search for topics will be effective if you focus on some limited options.

Capstone Project Ideas for Nursing

The activity field plays a decisive role, so nursing capstone project ideas are worth paying attention to. Use different nursing essay examples for your writing. Keep in mind that you can count on your advisor’s help when preparing the paper. You should make a difficult choice from the following suggested options:

Don’t be afraid to look for a variety of topics! Restrictions will prevent you from making the right choice. Make sure that the chosen topic corresponds to your worldview. You should do everything possible so you can express your ideas in a comprehensible way.

Capstone Project Ideas for Healthcare Administration

Personal interest helps in covering the discussed healthcare administration capstone project ideas. You rarely get an opportunity to highlight an acute and exciting issue. You should take advantage! Take a look at these topics:

Solving diverse tasks accounts for most of the administrators’ work. Can you get on well with patients and employees? Great! It will make it possible to achieve the set goals on the cheap. Professionalism without proper experience is not that important, after all.

Pharmacy Capstone Project Ideas

The search for capstone project ideas on pharmacy implies developing common issues from the field. Pharmacists are medical employees who communicate with patients more often than others. The friendly attitude and opportunity to help a visitor make them work tirelessly. The choice of the article direction can influence your working attitude in the future. Interesting ideas are as follows:

Popular non-drug treatments of certain diseases cause complications. Project on a topic that concerns it will help in attracting attention to it.

Psychology Capstone Project Ideas

It is tricky enough to choose capstone project ideas for Psychology. After all, the topic is based on a certain interest. You should forget titles you are not interested in. You will get a good grade if you describe a few opinions on the covered topic. You can finish the course in Psychology by working on one of the following topics:

Diverse topics can show you from a new side. It will allow you to put forward your own theory.

Education Capstone Project Ideas

You can show skills and capabilities for critical thinking upon deciding your capstone project ideas on Education. Those students who have chosen the right direction can get topics and continue with their professional growth. The search for worthy topics about education in a school or college will become a starting point for future achievements.

Mathematics Capstone Project Ideas

The right Math capstone project ideas will allow you to take a new look at application of calculations in everyday life. The following list will help you with finding a suitable idea:

Explaining the interest in mathematics is difficult. This doesn’t mean that there are no interesting ideas for the graduation paper. Theoretical studies ensure validity of results and allow you to control your research.

Capstone Project Ideas: High School

What are some quality high school capstone project ideas, you may ask. The education system is undergoing major changes. It is worth paying attention to the consequences of such innovations. Transition to remote learning allows to detect shortcomings in a new teaching method and develop problem-solving strategies. Choosing topics will be easier if you look through the list of options:

By studying relevant topics, you will be able to prepare for the beginning of professional activity in educational institutions.

Science Capstone Project Ideas

Science capstone project ideas depend on your direction, but this doesn’t mean that there are any restrictions. During the preparation of your final project, after completing your studies at Department of Technology, you should find new perspectives and consider those topics that potentially can make some contribution. Student must research their field of interest and focus on suitable options. Searching for information takes time, but the result is worth your effort. A small review will help you find a relevant topic.

Biology Capstone Project Ideas

By studying capstone project ideas for Biology, you can get answers for common questions. You can also find a simple solution for some issues. Thus, students can influence processes and prevent false information from spreading. Following these ideas will help get a dose of inspiration for you project: 

An attempt in creating a fascinating written piece will be a successful subject for studying reliable information from a few sources.

Can't find a fitting capston project topic idea? Give StudyCrumb's topic generator a try. 

Physics Capstone Project Ideas

People’s interest in Physics is easy to explain. Simple and logically explained processes can help you get rid of vague questions easily. Right choice of ap physics capstone project ideas from the following list will provide you with necessary inspiration when preparing your paper:

Any physical phenomenon that you are interested in can become the main subject of your study.

Data Science Capstone Project Ideas

Application of advanced technological methods for studying research results makes it possible to simplify project preparation, so you shouldn’t refuse such support. There is a variety of interesting capstone project ideas data science available:

Keep in mind that your resources are not limited, so decide on a topic you are interested in. The more data you collect, the more field work you should go through.

Business Capstone Project Ideas

Conducting business activities enables you to cover various capstone project ideas Business. Final results of work will show how well resources have been allocated. This will also teach you to reach a new level using limited opportunities. Choice of a management tool affects research results as well. It will be much easier to cover your ideas if you shift attention to aspects of your interest. There are no other ways in which you can make your paper effective.

Management Capstone Project Ideas

Paper preparation will begin immediately after choosing project management capstone ideas and obtaining required information. Any organization that offers its services for visitors can become a research object. Modern trends show that following topics will find readers’ response:

Creating a kind of application will enable you to find a way out of any difficult situations.

Topics for Capstone Project in Finance

Since students gain knowledge about commercial organizations’ financial activities, it will be impossible to avoid Finance capstone project. Those business areas that actively use financial resources are of particular interest. To choose worthy ideas, you can have look at suggested options:

You can collect information you will need for your paper online.

IT Capstone Project Ideas

Using a global system so you can get results is no longer a new method. That's why choice of capstone project ideas for information Technology should be taken seriously. After all, modern computers are used more and more often in everyday life. It can provide access to a variety of publications. Use resources so you can cover a topic and be prepared to search far and wide for needed information. An advantage of choosing this field will be an opportunity to influence the future of an industry.

Computer Science Capstone Project Ideas

When it comes to capstone project ideas, Computer Science just begs to use opportunities offered by the Internet. An attempt of finding a suitable topic will be successful if you start with studying list of options for writing a paper about software:

Application of technology has reached a new practical level. You shouldn’t just get stuck with your regular printed books and papers. Searching for exciting topics and conducting studies won’t take long.

Cybersecurity Capstone Project Ideas

So, cyber security capstone project ideas are a thing nowadays. Cybersecurity plays an important role in the modern world, so, should you choose this field of study, don't ignore any piece information that you can find. Developing an exciting project will enable you to improve your skills and put them into practice. You should pay special attention to the following topics:

Progressive developers should enhance modern skills and their practical application. To write a paper, you may need to get permission from an administrator, so you should keep that in mind.

Graphic Design Capstone Project Ideas

A graphic designer is a sought-after expert in the modern world and capstone design project ideas should be as good as they can. List of specialist’s main tasks includes developing logos and booklets, writing a video series for advertising products, and much more. An attempt to create a new graphical solution is the first level of skills improvement. Search for topics is the second important step, with the following to help you:

By developing unique design, you will attract large companies’ attention and become a confident competitor in this field.

Engineering Capstone Project Ideas

Among capstone project ideas, Engineering is one of the most interesting topics. It’s also widely promoted around the world. Available resources are used in full force, which enhances technical progress. It is still too early to stop at what has been achieved, so one should keep working and demonstrate great results. Search for topics takes quite long since this field is rapidly developing. Transition to alternative solutions to everyday tasks forces us to look for safe and working ways to achieve your set goal.

Mechanical Engineering Capstone Project Ideas

To develop capstone project ideas for Mechanical Engineering, you need to be interested in finding a solution. It’s impossible to do this without a proper interest in a breakthrough. Use knowledge you got to your advantage and take a closer look at suggested list of exciting topics:

An unbiased look at existing problems will enable you to show your creative potential and prove that your are suited to be a mechanical engineer.

Electrical Engineering Capstone Project Ideas

What can you say about capstone project ideas for Electrical Engineering? Electrical engineering plays a special role in everyday life. It also significantly improves quality of life. Technology studies will not only emphasize its importance but will have you understand a thing or two about its efficiency as well. You can choose topics from the following list:

Choosing a specific direction will help you demonstrate your potential and focus on solving everyday problems.

Computer Engineering Capstone Project Ideas

With how important technology is nowadays, it's no surprise that capstone project ideas for Computer Engineering are quite popular. Students are engaged in developing new software for solving a variety of tasks. Your capstone project should be aimed at introducing computer systems-based technologies. Popular topics consist of a few relevant topics:

Introduction of engineering solutions in everyday life can improve quality of services. It can provide necessary support to people with health problems.

Civil Engineering Capstone Project Ideas

Civil Engineering capstone project ideas are important if you are interested in seeing physical evidence of your work in real life. To develop the selected area, you will need to make efforts to improve conditions for people to live in. If you want to answer some concerns of accomplished professionals in this field, you need to prepare a project on one of the following topics:

A study of natural resources influence on service life and peculiarities of building construction and a careful study of underlying factors will result in an improvement in current results.

Final Thoughts on Ideas for Capstone Project

Choice of work field is based on conducting research on capstone project topics. Lack of interest has a negative effect on quality. It will be much easier to test your achievements and skills in the course using the latest topics. Or  buy capstone project online for a shortcut.

Our paper writing service can help to write a capstone project for you. We guarantee meeting the deadlines and deliver a project og of high quality.

FAQ about Capstone Project Ideas

1. are capstone projects hard.

Completing the course in chosen specialty implies mandatory preparation of capstone projects. The main challenge is to choose a topic and conduct research. As a student, you should demonstrate your skills in a chosen field. It’s enough to take the first step in right direction, though. The main problem is to find a really interesting topic.

2. What is the point of capstone?

Purpose of preparing a capstone project is to demonstrate your professional attitude to raised problems. Using acquired knowledge and an opportunity to make the world a better place are the main reasons to start preparing final project.

3. What is the difference between a thesis and a capstone project?

It is worth paying attention to differences between capstone project and a thesis. Basically, thesis is written when you're aiming for bachelor's and master's degrees. Meanwhile, capstone project is a piece of writing that you are expected to finish (typically) at the end of high school. Considering this, the length and scope can be different. For instance, capstone focuses on a narrower and more specific area. At the same time, thesis is written on much broader topic.

4. Is capstone required?

No, a capstone is usually not required. Some schools may make it mandatory for certain degrees, though. Choosing a specific topic means that student is willing to take risks. It shows that you try to achieve their goal. There is no other way to draw a final line in the chosen education program.


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Senior Capstone Project Ideas High School

Are you a student and got an assignment in your high school to write on a senior capstone project. But confused about selecting the good and appalling topic.

So here is the outstanding list for you prepared by the well-versed experts. Browse the whole list and pick the one that sets with your interest.

Senior Capstone Project Ideas for High School:

Pharmacy capstone project ideas:, engineering capstone project topics:, mba capstone project ideas:, management capstone project ideas:, education capstone project titles & ideas:, senior capstone project ideas in marketing:, accounting capstone project ideas:, information technology capstone project ideas:, nursing capstone project ideas:, political science capstone project ideas:, psychology capstone project ideas:, sports and entertainment capstone project ideas:, medicine senior capstone project ideas:, science and advancement in technology capstone project ideas:, various cultures capstone project ideas:, math capstone project ideas:, religion capstone project ideas:, custom essay writing services from students assignment help.

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70 Capstone Project Ideas for Any Student

What is a Capstone Project

How to choose killer capstone ideas, capstone project topics, nursing capstone project ideas, computer science capstone project ideas, information technology capstone topics, psychology capstone project ideas, management capstone project ideas, marketing capstone project ideas, education ideas for capstone projects, final thoughts.

Can't come up with a good capstone project idea? You are not alone in this. A capstone project is a challenging writing task for many students. It is not surprising because this academic work is essential for a future career. Therefore, if you aim to show in-depth knowledge in a field and demonstrate your core skills, make sure to pick an effective topic for capstone project. In our article, you will find a great variety of capstone project ideas in different fields of study. Use our guide to pick the topic you like most and create an outstanding academic paper.

A capstone project is a graduation project that students should present by the end of their senior year or course of study. This so-called culmination of degree allows showing what experience and insights they have gained at school. Capstone projects come in different shapes and sizes, depending on the specific academic requirements. A capstone project is beneficial to graduate students since it provides a unique opportunity to practice the following skills:

Some schools give a strict list of capstone project ideas you may choose from. Moreover, they provide a full list of requirements that a student needs to follow. However, sometimes you may select a theme related to your educational field yourself and write the paper using information you've already learned at the high school, college or university.

Having troubles looking for the best capstone project ideas ? Take it easy — check out these valuable tips that might come in handy during the brainstorming process:

We want to simplify the writing process and, thus, offer some great topics to choose from. There's no need to stay overnight brainstorming on good ideas for your graduate project. Check out the list of capstone topics below to save your time.

When you're required to write a sociology research paper, be prepared to work on a topic that is connected to people and society. You can choose from a variety of subjects including relationships, social norms, people's behavior, stereotypes, communication between different groups and individuals, a...

If you are studying Medicine and need worthy healthcare research topics for college, go no further! In this blog post, our proficient writers have compiled a useful list of health research ideas and suggestions on how to choose a decent topic. Select the one that you like most and be ready to nail a...

Things go the way we can pick relevant, up-to-date research paper topics these days. Be it an Instagram study or Kendrick Lamar’s influence on music in the last decade study – nowadays it is still a research writing. This piece of text will provide enough information and ideas to choose dazzling res...

Past Projects

2021 student projects, 2020 student projects, 2019 student projects, 2018 student projects, 2017 student projects, 2016 student projects, faculty research interests.

Faculty in the Georgia College Mathematics Department have research interests in variety of branches of mathematics and mathematics education. The following faculty descriptions offer students a glimpse at these interests relative to directing senior capstone projects.

Dr. Angel Abney's  research interests include preservice teachers’ models of students’ mathematics, effectiveness of preservice teacher education, mathematical knowledge for teaching, mathematical knowledge needed for teaching teachers and keeping women and minorities in the mathematical pipeline.

Dr. Martha Allen’s  areas of interest include number theory and cryptography. Previous projects have included examining a collection of proofs of the infinitude of the primes and investigating why primes are important, investigating the impact of ciphers on World War I and World War II, researching a modern day application of Euler’s Theorem, and considering applications of primitive roots and discrete logarithms in cryptography. A student desiring to work on a project with Dr. Allen should exhibit a strong work ethic, be highly self-motivated, be fluent in mathematical writing, and be proficient in LaTeX. In addition, to conduct research in number theory, a student should have successfully completed MATH 4110, and to conduct research in cryptography, a student should have taken or concurrently be taking MATH 4110 while enrolled in MATH 4989.

Dr. Guy Biyogmam's  research interests lie mainly in the field of non-associative algebras, combined with the areas of Leibniz Algebras, Algebraic Topology, Leibniz (Co)Homology, Invariant Theory and Homological Algebra. Possible projects will consist of using the Pirashvili spectral sequence to detect (non) relativistic invariants, which may be useful in the calculation of the Leibniz (co)homology of abelian extensions of semisimple Leibniz algebras. He also has some interest for BCK-algebras, Racks, Fuzzy set theory, and multilinear Lie algebras. These fields can generate several undergraduate projects. Some projects under my supervision to browse through are: "A study of subracks" (American Journal of Undergraduate Research, 13(2) (2014), 19-27) and "Centers of some non relativistic Lie algebra" (Rose-Hulman Undergraduate Mathematics Journal, Vol. 16, Issue 1, 2015).

Dr. George Cazacu’s  research interests include general topology, dynamical (poly)systems and stability theory, as well as algorithm complexity. He is tackling the P vs. NP problem in the hope that one day he will be able to fully understand it. A student interested in research under his guidance would have a considerable pool of topics to pick from, varying from rigorous understanding of abstract topological notions to attacking open problems or special, less explored cases of attractors in dynamical (poly)systems, or the study of some NP problems.

Dr. Marcela Chiorescu's  areas of research interest are in abstract algebra and its applications (in particular commutative algebra), in the history of mathematics (in particular the history of mathematics in Japan and China) and in the connection between mathematics and art (in particular the connection between mathematics and temari). A student desiring to work on a project on any of these areas should have successfully completed at least MATH 3030 and be proficient in LaTeX.

Dr. Rachel Epstein’s  primary area of research interest is mathematical logic, and in particular, computability theory.  In addition, she is interested in the connections between mathematics and origami, the history of mathematics around the world, and the application of mathematics to social issues such as gerrymandering and voting.  To say more about computability theory, it is the study of what is computable by a theoretical idealized computer (or Turing machine) and what isn’t.   Within the realm of the non-computable, we can classify mathematical objects such as real numbers by how much information they contain.  Computability theory can be applied to many areas of mathematics, such as abstract algebra or graph theory, as well as studied on its own.  To work on problems in computability theory, the only prerequisite would be Foundations of Mathematics (MATH 3030).  A subfield of computability theory that is closely linked to computer science is the study of randomness.  To work on randomness, Probability (MATH 4600) would be useful.  Other topics in mathematical logic include set theory, model theory, and Godel’s Incompleteness Theorems.  Students with an interest in computer science, philosophy, psychology, or physics could work on topics that combine computability theory or mathematical logic with those disciplines.

Dr. Susmita Sadhu's  research interest is in dynamical systems (differential equations) and its applications. More specifically, her research can be broadly classified into two sets: (i) studying and interpreting the behavior of solutions of nonlinear boundary value problems (which are ordinary differential equations with certain boundary conditions imposed on them), (ii) qualitatively analyzing and geometrically visualizing solutions of systems of differential equations that model some physical, biological or ecological phenomena. A student interested in learning classical theory of differential equations or interested in studying a problem that model an  ecological or a biological process should be comfortable with the material from one of the above sets. Mathematical tools such as Maple, MATLAB, XPPAUT will be frequently used and will be taught to the student. Programming capabilities are desirable, though not required.  Interested students are strongly encouraged to look at some undergraduate journals to get a sense of the nature of research done in this field.  Some possible papers to browse through are: "A predator prey model with disease dynamics" (Rose-Hulman Undergraduate Math Journal, vol 4, issue 1, 2003), "Long term dynamics for two three-species food web" (Rose-Hulman Undergraduate Math Journal, vol 4, issue 2,  2003), and "Introducing a scavenger onto a predator prey model" (Applied Math E-Notes, 2007), etc.

Dr. Brandon Samples'  areas of interest include representation theory (representing objects using methods of linear algebra), abstract algebra, number theory, graph theory, and mathematics education. A student wanting to work on a project with Dr. Samples in the pure mathematics setting should be interested and comfortable with material from at least a subset of the above mentioned branches of mathematics. A search of undergraduate mathematics journals (Rose-Hulman, College Math Journal, etc.) should allow the student to generate some possible topics. Previous projects have included topics coming from the study of Lie algebras associated to finite groups, combinatorics of finite graphs, generalized Fibonacci sequences, and generalizations of the Frobenius problem in number theory. A student wanting to work on a project within the realm of mathematics education should have thought about potential topics and searched the literature to get an idea of a possible framework. To get started, the student should have already looked at some mathematics education papers to get a sense for the nature of mathematics education research. Previous projects have included an analysis of conceptual versus procedural understanding in the context of story problems as well as assessing the efficacy of various teaching manipulatives at the undergraduate level.

Dr. Doris Santarone's  research interests lie in the areas of mathematical knowledge for teaching of inservice and preservice teachers, the mathematics content knowledge of preservice and inservice teachers, the mathematical knowledge needed for preservice teacher educators, and the evaluation of projects and programs for mathematics preservice teacher education.

Dr. Simplice Tchamna’s  primary area of interest is abstract algebra. He is interested in topics in commutative algebra.  Commutative algebra is the area of mathematics that studies commutative rings and other related topics such as module theory. Many areas of modern mathematics such as number theory, homological algebra, algebraic geometric, etc., use results from commutative algebra. A student wanting to work with him should complete (with at least a grade C) the two courses Math 3030 (Foundations of Mathematics) and Math 4081 (Abstract Algebra). He is also available to work with students wanting to explore topics in statistics. He is interested in techniques of collecting data to make predictions. In this case, the student should complete the two courses Math 1262 (Calculus I) and Math 2600 (Probability and Statistics).

Dr. Hong Yue’s  research interests lie in harmonic analysis related to function spaces, differential equations, fractal geometry and problem solving. Students who want to work on a project with Dr. Yue should have taken the course MATH 3030, Foundations of Mathematics. Also, if they are interested in a project in the setting of pure or applied mathematics, they should have taken​ at least one of courses MATH 4340, Differential Equations and MATH 4261, Mathematical Analysis. It is also encouraged that the students are good at a computer language or mathematical software, in particular, if they are interested in a topic in differential equations or fractal geometry.

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Student Projects Provide Real Solutions at Innovate to Grow Event

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Dozens of innovative ideas were on display at UC Merced's Innovate to Grow event May 11. The biannual event provides an opportunity for engineering students to showcase their capstone projects, in which teams work with local businesses and other institutions for several months to solve problems or challenges.

Students demonstrated their projects for judges and the public. The winning teams created the following: a more precise chute to direct fruit cocktail into a can, a safer hose key used in processing grapes into wine, a more efficient mowing system, an HVAC system for a building in Cairo, and portable headgear to detect concussion symptoms in the field.

Throughout the event, held in the gymnasium of the Joseph Edward Gallo Recreation and Wellness Center, students displayed and demonstrated projects as varied as using robots to transport payloads for farmers to making a piece of apparel that could hold multiple mastectomy drains after a mastectomy surgery so that the patient could be hands-free.

Sam Walley was part of a team that developed a remote eye examination tool for Valley Children's Hospital. Using a virtual reality headset, the system registered responses from volunteers and compared them to the normal range.

"It scans their eyes and looks at the full range of their view," Walley said. "All a patient has to do is put on the headset."

A monitor displayed what the patient sees and provides graphs denoting a normal range of measurements.

"If this bar is really low, the person may have astigmatism," said team member Austin Matthews.

Other teams displayed posters for ideas that had not yet reached reality. One of them was an idea for an app that would warn people in the path of potential flooding - predicated by the January levee break that impacted nearby Planada.

"Innovate to Grow provides a valuable opportunity for students to prepare for the engineering workforce," said Professor Alejandro Gutiérrez , who oversees the event. "Every project we have represents a real need by an external partner, so our students are literally gaining work experience while also completing academic requirements. Our program bridges the gap between the classroom and the engineering profession, and in doing so constitutes one of the strongest engines for social mobility at UC Merced."

After the day-long competition, the winners were named at an evening reception. They, and their project descriptions, are as follows:

Track 1 (Health) - Team 117: Vivian Nguyen, Christian Quintero Meza, Annie Ly, Caroline Amadet Barragan-Laguna, Kristal Navarro. The team was tasked by Valleys Children's Hospital to develop a portable headgear for early concussion diagnosis According to the Academy of Pediatrics, there are about 1.4 million cases of concussions annually. Often, the diagnosis of brain injury and timely intervention is delayed with decision making by non-healthcare providers in the field. The team's solution involves using dry EEG sensors with a P50 Auditory Stimulus Test. The P50 test records brain waves in response to repeated auditory stimuli every 500ms and analyzes them 50ms after the click. By measuring the percentage decrease of the brain waves, patients can be advised on whether medical attention is necessary in a timely manner.

Track 2 (Mechanics) - Team 114: Xaiver Vega, Lukas Fong, Ethan Murcia, Noah Johnson, Ray Medina. Every year, the American Society of Heating, Refrigerating and Air-Conditioning Engineers (ASHRAE) holds a design competition for HVAC systems. The team entered the Design Calculations category, designing and laying out an entire HVAC system for a building in Cairo, Egypt. Given CAD drawings, ASHRAE standards, and an OPR, the team provided heating and cooling load calculations, mechanical floor plan (duct size and layout, piping size and layout, etc.), coil sizing and selection, and Air Handling Unit selection.

Track 3 (AgTech) - Team 110: Alex Huynh, Galo Mora, Ricardo Diaz, Marco Garcia, Esmeralda Ochoa. California Transplants, an agricultural nursery company that specializes in growing transplants for commercial use, grows several vegetables that require repeated mowing to increase the strength and girth of the transplant. The current mowing system is time consuming, requires too many employees and costs too much to run. This team designed a system that is portable and will minimize operators and maximize savings. The machine is composed of a robot for travel and two large folding arms for suspended mowers. After testing with the robot and fabricated parts, the machine will then be implemented long-term into mowing operations.

Track 4 (Precision) - Team 107: Reid Mcleod, Antonio Villalobos, Kamila Ramirez, Govargiz Sayyad Shahbaz, Fernando Cruz. E. & J. Gallo Winery processes tons of grapes to make wine every year. To transform this much juice into wine takes multiple movements that require large, heavy, sanitary hoses. The brass couplings at the end of the hose are hooked up to stainless-steel pipe drops that connect tanks to processing equipment, or to other tanks for wine blending. The employees that attach or detach these hoses to the pipe drops are named "Rack & Blenders" and use a stainless-steel hose key. Hose connections are often tightly fastened and can take a large force to get on or off. Using the hose key with excessive force could cause a potential risk to the Rack & Blenders. If the hose key slips off the brass ears, it may cause injuries to the employees and damage surrounding equipment. The team has designed a greatly improved hose key that provides the Rack and Blenders with a safer and more robust and ergonomic tool to perform their labor-intensive task with reduced risk of injury. The tool is undergoing operational testing.

Track 5 (Food) Team 123: Brandon Baltazar, Adrian Rivera, Xerxes Zangeneh, Carlos Pedraza, Jessica Romero. Food processor Del Monte Foods, Inc. is losing monetary value due to its fruit spillage loss on conveyor lines and during the filling of the cans. To decrease the spillage that occurs on the conveyor line the team developed a can cover system that provides enough coverage to reduce spillage without increasing the probability of a jam occurring. The team also decreased fruit spillage during the filling of the cans by creating a chute to precisely direct the fruit into the cans, thus reducing the fruit spilled over the sides when filling.

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