## Department of Mathematics

- Math Research
- Senior Project

## Senior Project Marketplace

## Senior project ideas

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

## High School Mathematics Curriculum Development

## Middle School Mathematics Curriculum Development

## Other project ideas

## Contact info

## Samuel Coskey - Set theory, logic, and combinatorics

Combinatorics and graph theory.

## Algebra or analysis or geometry

## Math education

## Contact Info

## Jens Harlander - Topology and Algebra (Group Theory)

Jens Harlander Faculty Profile Page

## Uwe Kaiser - Geometric and Algebraic Topology, Quantum Computing

## Tangles and Electrical Networks

## Robotics and Topology

## Analysis Situs

## 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.

https://zteitler.github.io/advising/senior_thesis/

## 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,...an 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 www.cse.iitk.ac.in 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.

## OPUS Open Portal to University Scholarship

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 kaggle.com. , 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.

## Add Project Key Words

## Capstone Projects for High School Students

Padya Paramita

February 10, 2020

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

## Quick Navigation

❔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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## Capstone Project Ideas That Will Get You That Sweet "A" Grade

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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

## Capstone Project Ideas for Nursing

- Emergency care: existing practices.
- Reasons for nurse shortage.
- Peculiarities of working in medical institutions.
- Focusing on the patients’ needs.
- Pain management: effective practice.
- The best instructions for nurses.
- Value of working in medical institutions.
- Personal approach to visitors.
- Required knowledge before you start the job.
- Professional burnout: The reasons.

## Capstone Project Ideas for Healthcare Administration

- Staff shortage: Solving the situation.
- Preparing staff for work: Where you should start.
- Stress resistance and its importance for work.
- Communication with patients as an integral responsibility.
- Professional skills’ application.
- Process management's challenges.
- Professional deformation: The signs.
- Mandatory management skills.
- Mind flexibility for finding compromises.
- Insufficient preparation for a surgery and its consequences.

## Pharmacy Capstone Project Ideas

- Antibiotics efficiency.
- Traditional medicine: the importance.
- Taking medications: consequences.
- Immunosuppressants and how they affect health.
- Probiotics to combat the antibiotics effects.
- Taking medications: side effects.
- Resources conservation for producing safe medications.
- Search for alternative solutions: Pros and cons.
- Traditional treatment: consequences.

## Psychology Capstone Project Ideas

- Incurable diseases' impact on psychological health.
- Are gender and a propensity for depression linked?
- Algorithm for forming habits.
- Influence of upbringing in Rainbow Family on the reality assessment.
- Television's impact on the patients' well-being.
- Obesity and what psychological problems it hides.
- Stress and its impact on different groups of people.
- Psychological development: key stages.
- Psychological improvement under external factors.
- Hyperactivity: Who is to “blame”.

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

## Education Capstone Project Ideas

## Mathematics Capstone Project Ideas

- Hungarian approach in developing educational programs.
- Ranking methods.
- Partial and complex process interventions: comparison.
- The process of crystal structure formation.
- Process optimization using a mathematical approach.
- The number pi discovery history and development in modern science.
- Unproven theories: Why failure.
- Application of constants in calculations and their impact on the result.
- Mathematical description of the evacuation.
- Development of mathematics in the past decade.

## Capstone Project Ideas: High School

- Why should one attend extracurricular activities?
- Why is discrimination at school constantly increasing?
- What are the reasons for school children being more violent?
- Discipline at school: effective ways to combat disorder.
- Does respect for a teacher mean having no personal opinion?
- Conducting academic lessons while studying at school.
- Results of remote learning.
- Classroom modernization and its consequences.
- Advantages of using modern learning technologies.
- How do social networks affect the learning process at senior schools?

## Science Capstone Project Ideas

## Biology Capstone Project Ideas

- Reasons for different gestation periods among animals.
- Justification of gender identity by genetic specifics.
- Impact of alcohol abuse on health.
- Time required for habits to cause damage.
- Donating a human body for research.
- Which role does a human play in natural world?
- Biology of mental disorders (schizophrenia, depression).
- Viruses spread by rodents.
- Creating human body atlases: pros and cons.
- Three-dimensional modeling of life processes.

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

## Physics Capstone Project Ideas

- Real size of quantum world: how big is it?
- Interesting phenomena that are difficult to explain.
- Simple physical experiments at home.
- Interesting physics theory that can surprise.
- How does one demonstrate induction law?
- Lagrange multipliers: what is it?
- Gaps in black holes studies.
- Can everything be explained by physics laws?
- Crystal structure and how one can change it.
- What is gravitational attraction of planets like?

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

## Data Science Capstone Project Ideas

- Forecast of health condition based on shopping list.
- How does information storage influence a person’s everyday life?
- Weather forecast based on historical data.
- Amount of solar energy, taking satellite images into account.
- How does one simplify false news detection?
- Determining a dog breed using a neural network.
- Analysis of users’ mood based on certain data.
- Convenient ways of storing information.
- Options for finding delicious food using data.

## Business Capstone Project Ideas

## Management Capstone Project Ideas

- Corporate strategy and how one can conduct development.
- Profitability and capital investments: business value.
- Ways of solving conflict situations.
- Business activities and wrong decisions.
- How one can solve a professional conflict.
- Ways of developing a corporate mind.
- Assessment of key processes in a clinic.
- Managing different levels of administrator.
- Advertising campaign: right way of project management.
- Ethical thinking and management.

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

## Topics for Capstone Project in Finance

- Common financial problems.
- Influence of financial resources on global economy.
- How one can manage risks at minimum losses.
- Corporate finance: how one can allocate resources.
- Internal financial markets and their interrelation with global resources.
- Investment analysis.
- Budget funds management systems.
- How one can decide on the advisability of investments?
- Electronic payment: how one can use it to business advantage.
- Developing a marketing plan to attract investors.

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

## IT Capstone Project Ideas

## Computer Science Capstone Project Ideas

- Automatic reporting.
- Developing computer software for registration.
- Studying data of a clinic’s clients.
- Using programs for enhancing work efficiency.
- Payment verification and ways of protecting accounts.
- Online customer survey system.
- How one can restore lost data?
- How one can prevent loss of important information?
- Personal data protection by using software.
- Main reasons for the importance of using programs.

## Cybersecurity Capstone Project Ideas

- Keylogger development and use of software in work.
- Data traffic analysis for process optimization.
- Network traffic and how to prevent hackers from accessing it.
- Personal data protection options.
- Decoding popular ciphers.
- Development of a program for data encryption.
- Creating antivirus security programs.
- Search for mistakes made on Internet websites.
- Practical skills to find system shortcomings.
- Software preparation for higher security.

## Graphic Design Capstone Project Ideas

- Ways to unify characters.
- Animation and cartoon creation.
- Unique business project design.
- Improving a developed object.
- Conditions that affect design efficiency.
- Three-dimensional character modeling.
- Modern programs for creating graphics.
- Logo development depending on field.
- Individual graphic projects.
- Graphic design as a way of communicating with clients.

## Engineering Capstone Project Ideas

## Mechanical Engineering Capstone Project Ideas

- Remote-controlled vehicles.
- Automatic limbs: application.
- Using a mobile device to control movements.
- Development of mechanical skills to improve performance.
- Drinking water purification using a drive.
- Chain mechanisms: how to use engines for work.
- Working with devices: peculiarities.
- Performing mechanical actions instead of a human.
- Ways to improve a mechanical engine performance.
- Why does field development play an important role?

## Electrical Engineering Capstone Project Ideas

- Solar panel management.
- Creating a hybrid vehicle.
- Advantages and disadvantages of using electricity.
- Ways to extend solar panels' life.
- Systems for detecting red traffic light signals.
- Importance of electricity in everyday life.
- How to use solar panels at home?
- Solar energy and ways to use it.
- Devices for energy accumulation.
- Electric power: disadvantages of power source.

## Computer Engineering Capstone Project Ideas

- Machine learning or how a computer can recognize a cat.
- Security system with lock function.
- Using modern registration methods.
- Automatic schedule creation: results of development.
- Selection of music considering emotional state.
- Facial emotion recognition system.
- A knowledge assessment system considering students' level of knowledge.
- Remote monitoring of vital activity systems.
- Ways to create an image with encrypted text.
- How to detect a hacker attack?

## Civil Engineering Capstone Project Ideas

- Foundation analysis.
- Stages of designing high-rise buildings.
- Carrying out seismic activity calculations.
- Project management in construction field.
- Building design.
- Performing training of resistance to loads.
- Quantitative shooting to detect deficiencies.
- Advantages and disadvantages of seismic research.
- Open soil and design peculiarities.
- Types of soils and their influence on buildings’ duration.

## Final Thoughts on Ideas for Capstone Project

## FAQ about Capstone Project Ideas

1. are capstone projects hard.

## 2. What is the point of capstone?

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

## 4. Is capstone required?

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## Senior Capstone Project Ideas High School

## Senior Capstone Project Ideas for High School:

- Discuss the disciplinary measures in schools.
- Can we see virtual high schools as the future of learning?
- What do you understand by multicultural education?
- Poverty – plan and organize a toy drive for a low-income neighborhood or local orphanage.
- Is the use of cell phones in the classroom legal?
- What are the factors that affect the use of conventional medicine?
- What do you understand by Pharmacodynamic and pharmacokinetic principles of antibiotics?
- Monotherapy and drug resistance.
- What do you understand by precision dosing?
- What is the antibiotic resistance pattern?
- What are the improvements needed in racing cars?
- The pros and cons of electric energy.
- How we can transmit the geological data effectively?
- Crucial Engineering recommendations.
- How can we effectively apply engineering management systems to control quality?
- Utility bills and product promotion.
- An assessment of customer engagement for a selected company.
- Analysis of different business practices applicable in certain industries.
- The advantages of e-learning for professional certification.
- The significance of supplier relationship management in businesses.
- Key human resource management of 2019.
- Role of project management in promotion campaigns.
- The importance of crisis management to continue the businesses effectively.
- The key challenges occurred in multinational management and the best strategies to avoid them.
- The challenges in International management.
- Effective classroom management and its impact on student’s behavior.
- Academic use of technology and social media in the classrooms.
- Education of asthma for nurses.
- Advantages and disadvantages of sex education.
- Discuss the theoretical background of distant learning.
- Importance of e-commerce to grow your business.
- Define green marketing and its beneficial strategies.
- How To Find A Balance Between Online and Offline Shopping.
- The principles and values of international marketing campaigns.
- The change in buying preferences with a geographical location.
- The impact of accounting on income taxes.
- Discuss accounting theories for applied management.
- Various forms of accounting systems are utilized in organizations all around the world.
- Importance of accounting for the success of a business.
- The effective role of ethical decision-making.
- Voice and text recognition systems.
- All systems for business decision-making.
- What do you understand by data warehousing and its role to alter the information systems?
- All you need to know about information logistics, data warehousing, and data mining.
- The process to handle cyberbullying .
- The connection between shift hours and quality of nurse’s services.
- Best practices for healthcare workers to deal with critical care patients and emergencies.
- Methods Of Preventing The Dysfunctional Behaviours Among Patients Suffering From Dementia.
- Do you see cow’s milk as a balanced diet on its own?
- Research on other people’s perceptions of the role of nurses in society.
- The advantages of developing a global relationship with different countries.
- The function of project management is ineffective political campaigns.
- Principles of socialism and communism.
- The role of the governance system in the US.
- The functioning of the UN in maintaining peace in the world.
- Discuss borderline personality disorder.
- The factors are responsible for short and long-term memory.
- The best cure for Schizophrenia.
- How can we relate stress and physical illness?
- Critical stages of human development and growth.
- Online blogs instead of newspapers are the best places to get credible sports reviews today!
- Is it beneficial to keep using animals in sports?
- Depict the reason why soccer or football is the most famous sport around the world.
- The role of violent games in making the kids angry and cruel.
- Why do people prefer online blogs over newspapers nowadays to get reviews in sports?
- The possible reasons for antibiotic resistance.
- What do you understand by life-sustaining therapy?
- Discuss health diversity.
- The best prevention for cruel scientific testing of animals.
- How adopting vaccination measures for kids is useful?
- The basic science procedures.
- The prevention of online personal data getting corrupted.
- Discuss black hole singularity.
- Pros and cons of Nanomedicine.
- Benefits of Hormone growth therapy.
- The significance of critical race theory.
- The re-comprehension of past occurrences and procedures.
- The roots of anti-Semitism.
- What should school administrators do to punish perpetrators of bullying?
- Cultural revolution throughout history.
- The areas where we can apply math.
- The role of algorithms in math.
- What is the connection between math and science?
- The significance of math in today’s world.
- Depict the most complicated math problems.
- The role of religion in changing the perception towards the world.
- What do you understand by creationism?
- Discuss Christianity.
- What is the interpretation of bisexuality in the Bible?
- What is the reason for war in the Middle East? Is it religion?

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## What is a Capstone Project

- Stick to the problem-solving objective. The topic you choose should help you solve a complex problem. It is the primary aim of your investigation.
- Turn writing into an engaging activity. Determine the fascinating subject in the field of study. This way, you will be interested in the writing process.
- Rely on previous research. Consider the material you already have when you are working on coursework and practical material.
- Estimate the sources. Assess both the history of the research topic and current analytical reviews to find hypothetical questions within your study framework.
- Pick informative topics. It's better to choose subjects that offer enough information and allow you to complete in-depth research.
- Plan your time wisely . Give yourself enough time to tackle this assignment. Be aware that it may take much longer than college academic papers.
- Engage your reader. An intriguing topic covering a significant issue is the key to success. Choose those themes that are important to society.
- Show your experience in the field. Your work's quality depends on how well you know the topic, so choosing a too complicated or too easy subject would be a bad idea.
- Stay precise in your writing. The topic should be narrow and specific. Don't use a too broad subject because you won't be able to address a particular issue.
- Seek advice from a teacher. Consult with the instructor, listen to his or her opinion regarding the chosen subject for your project.

- Why is breastfeeding a good option for infants?
- Innovations in diagnosing testing.
- An efficient nursing program aimed to improve the medical care of older people.
- The most widespread sexually transmitted diseases.
- Prevention methods for type 3 diabetes.
- Comparison of current healthcare programs and healthcare in the past.
- The nursing training pan that improves the quality of medical assistance.
- Why does HPV cause increased patients' awareness and vaccination?
- The ways to create a specific regimen for proper immunization.
- Nursing care analysis, new strategies, and methods of improvement.
- Development of software that coordinates retail business supply and sales.
- The role of online software in the real estate development company.
- The use of computers and other gadgets in modern education.
- Data recovery for information systems
- Computer disaster prevention.
- The role of contemporary technology in protection from identity theft.
- Game theory in computer analysis and algorithms.
- Internet security measures and current protective systems.
- Math placement test development.
- Mobile education apps for students.
- The use of object detection and recognition algorithms in surveillance equipment.
- The role of data mining in modern businesses.
- The significance of cloud computing
- The Internet of Things and its importance
- The comparison of manual and automated testing
- Data security measures
- The principles of cyber-physical system
- Cybersecurity measures in modern businesses
- The role of Artificial Intelligence in economy
- Network management and monitoring
- Why does stress affect our personality and influence our behavior?
- What factors cause suicidal behavior?
- Social interaction of modern teenagers.
- The difference between short and long-term memory?
- Why are some people addicted to depression? (consult: research paper on depression )
- How does the environment influence our personality?
- Crucial stages of human growth and psychological development.
- Violence in games and its effect on teenagers and their learning capacity.
- The impact of bipolar disorder on human's life
- The importance of psychology in modern businesses
- The influence of crisis management on small business
- Project management in the shipbuilding industry.
- Women empowerment in the financial sector.
- The latest management system innovations in the business.
- The efficiency of the franchising system in various businesses.
- Globalization and customization: what is the difference?
- The necessity of risk management for business
- Customer service in restaurants: detailed analysis.
- E-commerce development and recent trends.
- How to choose the best strategy in public relations?
- The role of social media in marketing
- The necessity of blogging for traffic generation
- Content marketing strategies used by various businesses
- Behavior knowledge and effective relationships
- Business-to-business marketing methods
- Business-to-customer marketing strategies
- The significance of jingles in advertising
- The ways of building brand awareness
- Recent trends in product loyalty
- The most effective account-based tactics
- Is bilingual education efficient?
- The influence of degree level on a career.
- Why is classroom management essential for students' behavior?
- How can teachers motivate students to get higher results?
- Educational models that require changes.
- Development projects that can increase students' achievements.
- Distant learning as a good option for some students.
- Elementary school programs for personal growth.
- How to improve the psychological environment in high schools?
- The use of popular games in modern education.

## Past Projects

- Arts & Music
- English Language Arts
- World Language
- Social Studies - History
- Special Education
- Holidays / Seasonal
- Independent Work Packet
- Easel by TPT
- Google Apps

## Interactive resources you can assign in your digital classroom from TPT.

## Easel Activities

## Easel Assessments

## All Formats

Resource types, all resource types, results for capstone projects.

## Accounting Simulation Capstone Project - Final or End of the Year / Semester

## Capstone Engineering Design Project (Engineering/Robotics/CAD/CTE/CS)

## Capstone Project - Solving Societal Problems

## Capstone Project (Career Research, Creative Expression, Autobiography, Service)

## Montessori: Imaginary Island Capstone Project (Upper Elementary)

## Montessori Imaginary Island Geography Capstone Project --an album

## Business Management Capstone Project

## Personalized Learning Project ( Cap Stone ) (Senior Project ) (Independent Study)

## Triangle Factory Fire Capstone Project

## Social Media Marketing Audit Project - Capstone Business Project

## Todo Sobre Mí Capstone Project for Spanish 1

## Capstone Magazine Project : "The Breadwinner" by Deborah Ellis

## Capstone Project - Bundle

## 108 CAPSTONE / Project Ideas - Use with High School or Middle School!

## Shark Tank Business Cap Stone Calculations Project

## AP Spanish Language and Culture Capstone Project

## Chemistry End of Year Capstone Project

## Engaging Students Through Capstone Projects

## Senior Capstone Literacy Project Experience

## SEI Math Capstone Project

## Guidelines for Preparing Student/Senior Projects / Capstones

## Lesson Plan: Differentiated Student Product Climate Change Capstone Project

## Capstone Project Description with Dates and Summary of Goals

TPT empowers educators to teach at their best.

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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.

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 ...

International Baccalaureate Mathematics, Advanced Placement Mathematics, and Dual Credit Mathematics Courses - An In Depth Look, Lawrence Benjamin Jaskunas. PDF. Strategies for Overcoming Math Anxiety in Developmental Math Students at Community Colleges, Nika Alex. PDF. The Necessity of Fundamental Math in College, Spencer A. McDuffy, Sr.

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. Abstract: Let V = {p_1, · · · , p_k} be a finite set of points in P^2.

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. Start a band, write your own songs, even put them on Spotify or Apple Music (and sign up for performances!); Study the effect of music therapy on children ...

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.

Management Capstone Project Ideas. Evaluation of free clinic process. The role of project management in effective political campaigns. The practice of ethical thinking in administration. Modern strategies for rate of return and capital investment. The importance of conflict administration for big companies.

Math Capstone Ideas. I am about to start my senior year as an undergraduate. As part of the honors math program, i need to do a capstone (or thesis) over the course of the year. I have done a fair amount of modeling and find that very interesting, but I also am very interested in some pretty fundamental questions (especially involving prime ...

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: Hungarian approach in developing educational programs. Ranking methods. Partial and complex process interventions: comparison.

12 subscribers in the capstone_project community. Capstone Project - EditaPaper.com. Advertisement Coins. 0 coins. Premium Powerups . Explore . ... MATH CAPSTONE PROJECT IDEAS. paperhelp.space. comments sorted by Best Top New Controversial Q&A Add a Comment . More posts you may like.

You have the choice of 3 project from which to choose. Geometry students can choose option 1 or option 3. Option 1 is based more on algebra content viz. parabola. Option 3 is based on volume, area, surface area and different object etc. Option 1. Capstone_project_2016 (Algebra/Pre-Calculus) - Example of growth project. Option 2.

Education Capstone Project Titles & Ideas: Effective classroom management and its impact on student's behavior. Academic use of technology and social media in the classrooms. Education of asthma for nurses. Advantages and disadvantages of sex education. Discuss the theoretical background of distant learning.

List of 100 Education Capstone Project Ideas. How and why a degree level impacts career. High school English classroom: Academic uses of social media technology. Tools and benefits of bilingual education. Choosing algebra as a civil right.

As part of the Capstone course, each student proposes and carries out an individual research project under the direction of a faculty advisor. Examples of student projects are listed below. Fall 2022. Modeling Point Differential in the NBA with Linear Regression; An Exploration of the Cantor-Zassenhaus Algorithm

critical thinking. problem-solving skills. time management. promptness. teamwork. communication skills. persuasive 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.

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).

The capstone project for the STEM strand is designed for technology, engineering, and math. This is necessary so that the student can think critically in the future. ... STEM capstone project ideas for all students. Design and research work at school is a new, innovative method that combines educational and cognitive components, games ...

Student-Adviser Mathematics Capstone Project Contract Student: Adviser: Semester: Year: Project Topic/Title: This is an optional contract to be agreed upon between the student and their adviser. If applicable, this contract should be lled out before the add/drop date of the semester. Set a date for any or all of the

Jan 22, 2019 - Explore Steve Mays's board "AQR Capstone Project Ideas" on Pinterest. See more ideas about math classroom, middle school math, math projects.

4. $10.00. PDF. Capstone Project: - A culminating experience calling upon students to utilize a vast amount of skills and knowledge learned throughout high school. - The projects in this book will ask students to research a chosen topic, create their own experiment, analyze the results of this experiment, and disse.

May 24, 2023. Engineering capstone projects displayed at biannual event. 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 ...