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What Students Are Saying About the Value of Math

We asked teenagers: Do you see the point in learning math? The answer from many was “yes.”

By The Learning Network

“Mathematics, I now see, is important because it expands the world,” Alec Wilkinson writes in a recent guest essay . “It is a point of entry into larger concerns. It teaches reverence. It insists one be receptive to wonder. It requires that a person pay close attention.”

In our writing prompt “ Do You See the Point in Learning Math? ” we wanted to know if students agreed. Basic arithmetic, sure, but is there value in learning higher-level math, such as algebra, geometry and calculus? Do we appreciate math enough?

The answer from many students — those who love and those who “detest” the subject alike — was yes. Of course math helps us balance checkbooks and work up budgets, they said, but it also helps us learn how to follow a formula, appreciate music, draw, shoot three-pointers and even skateboard. It gives us different perspectives, helps us organize our chaotic thoughts, makes us more creative, and shows us how to think rationally.

Not all were convinced that young people should have to take higher-level math classes all through high school, but, as one student said, “I can see myself understanding even more how important it is and appreciating it more as I get older.”

Thank you to all the teenagers who joined the conversation on our writing prompts this week, including students from Bentonville West High School in Centerton, Ark, ; Harvard-Westlake School in Los Angeles ; and North High School in North St. Paul, Minn.

Please note: Student comments have been lightly edited for length, but otherwise appear as they were originally submitted.

“Math is a valuable tool and function of the world.”

As a musician, math is intrinsically related to my passion. As a sailor, math is intertwined with the workings of my boat. As a human, math is the building block for all that functions. When I was a child, I could very much relate to wanting a reason behind math. I soon learned that math IS the reason behind all of the world’s workings. Besides the benefits that math provides to one’s intellect, it becomes obvious later in life that math is a valuable tool and function of the world. In music for example, “adolescent mathematics” are used to portray functions of audio engineering. For example, phase shifting a sine wave to better project sound or understanding waves emitted by electricity and how they affect audio signals. To better understand music, math is a recurring pattern of intervals between generating pitches that are all mathematically related. The frets on a guitar are measured precisely to provide intervals based on a tuning system surrounding 440Hz, which is the mathematically calculated middle of the pitches humans can perceive and a string can effectively generate. The difference between intervals in making a chord are not all uniform, so guitar frets are placed in a way where all chords can sound equally consonant and not favor any chord. The power of mathematics! I am fascinated by the way that math creeps its way into all that I do, despite my plentiful efforts to keep it at a safe distance …

— Renan, Miami Country Day School

“Math isn’t about taking derivatives or solving for x, it’s about having the skills to do so and putting them to use elsewhere in life.”

I believe learning mathematics is both crucial to the learning and development of 21st century students and yet also not to be imposed upon learners too heavily. Aside from the rise in career opportunity in fields centered around mathematics, the skills gained while learning math are able to be translated to many facets of life after a student’s education. Learning mathematics develops problem solving skills which combine logic and reasoning in students as they grow. The average calculus student may complain of learning how to take derivatives, arguing that they will never have to use this after high school, and in that, they may be right. Many students in these math classes will become writers, musicians, or historians and may never take a derivative in their life after high school, and thus deem the skill to do so useless. However, learning mathematics isn’t about taking derivatives or solving for x, it’s about having the skills to do so and putting them to use elsewhere in life. A student who excels at calculus may never use it again, but with the skills of creativity and rational thinking presented by this course, learning mathematics will have had a profound effect on their life.

— Cam, Glenbard West

“Just stop and consider your hobbies and pastimes … all of it needs math.”

Math is timing, it’s logic, it’s precision, it’s structure, and it’s the way most of the physical world works. I love math — especially algebra and geometry — as it all follows a formula, and if you set it up just right, you can create almost anything you want in at least two different ways. Just stop and consider your hobbies and pastimes. You could be into skateboarding, basketball, or skiing. You could be like me, and sit at home for hours on end grinding out solves on a Rubik’s cube. Or you could be into sketching. Did you know that a proper drawing of the human face places the eyes exactly halfway down from the top of the head? All of it needs math. Author Alec Wilkinson, when sharing his high school doubting view on mathematics, laments “If I had understood how deeply mathematics is embedded in the world …” You can’t draw a face without proportions. You can’t stop with your skis at just any angle. You can’t get three points without shooting at least 22 feet away from the basket, and get this: you can’t even ride a skateboard if you can’t create four congruent wheels to put on it.

— Marshall, Union High School, Vancouver, WA

“Math gives us a different perspective on everyday activities.”

Even though the question “why do we even do math?” is asked all the time, there is a deeper meaning to the values it shares. Math gives us a different perspective on everyday activities, even if those activities in our routine have absolutely nothing to do with mathematical concepts itself. Geometry, for instance, allows us to think on a different level than simply achieving accuracy maintains. It trains our mind to look at something from various viewpoints as well as teaching us to think before acting and organizing chaotic thoughts. The build up of learning math can allow someone to mature beyond the point where if they didn’t learn math and thought through everything. It paves a way where we develop certain characteristics and traits that are favorable when assisting someone with difficult tasks in the future.

— Linden, Harvard-Westlake High School, CA

“Math teaches us how to think.”

As explained in the article, math is all around us. Shapes, numbers, statistics, you can find math in almost anything and everything. But is it important for all students to learn? I would say so. Math in elementary school years is very important because it teaches how to do simple calculations that can be used in your everyday life; however middle and high school math isn’t used as directly. Math teaches us how to think. It’s far different from any other subject in school, and truly understanding it can be very rewarding. There are also many career paths that are based around math, such as engineering, statistics, or computer programming, for example. These careers are all crucial for society to function, and many pay well. Without a solid background in math, these careers wouldn’t be possible. While math is a very important subject, I also feel it should become optional at some point, perhaps part way through high school. Upper level math classes often lose their educational value if the student isn’t genuinely interested in learning it. I would encourage all students to learn math, but not require it.

— Grey, Cary High School

“Math is a valuable tool for everyone to learn, but students need better influences to show them why it’s useful.”

Although I loved math as a kid, as I got older it felt more like a chore; all the kids would say “when am I ever going to use this in real life?” and even I, who had loved math, couldn’t figure out how it benefits me either. This was until I started asking my dad for help with my homework. He would go on and on about how he used the math I was learning everyday at work and even started giving me examples of when and where I could use it, which changed my perspective completely. Ultimately, I believe that math is a valuable tool for everyone to learn, but students need better influences to show them why it’s useful and where they can use it outside of class.

— Lilly, Union High School

“At the roots of math, it teaches people how to follow a process.”

I do believe that the math outside of arithmetic, percentages, and fractions are the only math skills truly needed for everyone, with all other concepts being only used for certain careers. However, at the same time, I can’t help but want to still learn it. I believe that at the roots of math, it teaches people how to follow a process. All mathematics is about following a formula and then getting the result of it as accurately as possible. It teaches us that in order to get the results needed, all the work must be put and no shortcuts or guesses can be made. Every equation, number, and symbol in math all interconnect with each other, to create formulas that if followed correctly gives us the answer needed. Everything is essential to getting the results needed, and skipping a step will lead to a wrong answer. Although I do understand why many would see no reason to learn math outside of arithmetic, I also see lessons of work ethics and understanding the process that can be applied to many real world scenarios.

— Takuma, Irvine High School

“I see now that math not only works through logic but also creativity.”

A story that will never finish resembling the universe constantly expanding, this is what math is. I detest math, but I love a never-ending tale of mystery and suspense. If we were to see math as an adventure it would make it more enjoyable. I have often had a closed mindset on math, however, viewing it from this perspective, I find it much more appealing. Teachers urge students to try on math and though it seems daunting and useless, once you get to higher math it is still important. I see now that math not only works through logic but also creativity and as the author emphasizes, it is “a fundamental part of the world’s design.” This view on math will help students succeed and have a more open mindset toward math. How is this never-ending story of suspense going to affect YOU?

— Audrey, Vancouver, WA union high school

“In some word problems, I encounter problems that thoroughly interest me.”

I believe math is a crucial thing to learn as you grow up. Math is easily my favorite subject and I wish more people would share my enthusiasm. As Alec Wilkinson writes, “Mathematics, I now see, is important because it expands the world.” I have always enjoyed math, but until the past year, I have not seen a point in higher-level math. In some of the word problems I deal with in these classes, I encounter problems that thoroughly interest me. The problems that I am working on in math involve the speed of a plane being affected by wind. I know this is not riveting to everyone, but I thoroughly wonder about things like this on a daily basis. The type of math used in the plane problems is similar to what Alec is learning — trigonometry. It may not serve the most use to me now, but I believe a thorough understanding of the world is a big part of living a meaningful life.

— Rehan, Cary High School

“Without high school classes, fewer people get that spark of wonder about math.”

I think that math should be required through high school because math is a use-it-or-lose-it subject. If we stop teaching math in high school and just teach it up to middle school, not only will many people lose their ability to do basic math, but we will have fewer and fewer people get that spark of wonder about math that the author had when taking math for a second time; after having that spark myself, I realized that people start getting the spark once they are in harder math classes. At first, I thought that if math stopped being required in high school, and was offered as an elective, then only people with the spark would continue with it, and everything would be okay. After thinking about the consequences of the idea, I realized that technology requires knowing the seemingly unneeded math. There is already a shortage of IT professionals, and stopping math earlier will only worsen that shortage. Math is tricky. If you try your best to understand it, it isn’t too hard. However, the problem is people had bad math teachers when they were younger, which made them hate math. I have learned that the key to learning math is to have an open mind.

— Andrew, Cary High School

“I think math is a waste of my time because I don’t think I will ever get it.”

In the article Mr. Wilkinson writes, “When I thought about mathematics at all as a boy it was to speculate about why I was being made to learn it, since it seemed plainly obvious that there was no need for it in adult life.” His experience as a boy resonates with my experience now. I feel like math is extremely difficult at some points and it is not my strongest subject. Whenever I am having a hard time with something I get a little upset with myself because I feel like I need to get everything perfect. So therefore, I think it is a waste of my time because I don’t think I will ever get it. At the age of 65 Mr. Wilkinson decided to see if he could learn more/relearn algebra, geometry and calculus and I can’t imagine myself doing this but I can see myself understanding even more how important it is and appreciating it more as I get older. When my dad was young he hated history but, as he got older he learned to appreciate it and see how we can learn from our past mistakes and he now loves learning new things about history.

— Kate, Cary High School

“Not all children need to learn higher level math.”

The higher levels of math like calculus, algebra, and geometry have shaped the world we live in today. Just designing a house relates to math. To be in many professions you have to know algebra, geometry, and calculus such as being an economist, engineer, and architect. Although higher-level math isn’t useful to some people. If you want to do something that pertains to math, you should be able to do so and learn those high levels of math. Many things children learn in math they will never use again, so learning those skills isn’t very helpful … Children went through so much stress and anxiety to learn these skills that they will never see again in their lives. In school, children are using their time learning calculus when they could be learning something more meaningful that can prepare them for life.

— Julyssa, Hanover Horton High School

“Once you understand the basics, more math classes should be a choice.”

I believe that once you get to the point where you have a great understanding of the basics of math, you should be able to take more useful classes that will prepare you for the future better, rather than memorizing equations after equations about weird shapes that will be irrelevant to anything in my future. Yes, all math levels can be useful to others’ futures depending on what career path they choose, but for the ones like me who know they are not planning on encountering extremely high level math equations on the daily, we should not have to take math after a certain point.

— Tessa, Glenbard West High School

“Math could shape the world if it were taught differently.”

If we learned how to balance checkbooks and learn about actual life situations, math could be more helpful. Instead of learning about rare situations that probably won’t come up in our lives, we should be learning how to live on a budget and succeed money-wise. Since it is a required class, learning this would save more people from going into debt and overspending. In schools today, we have to take a specific class that doesn’t sound appealing to the average teenager to learn how to save and spend money responsibly. If it was required in math to learn about that instead of how far Sally has to walk then we would be a more successful nation as a whole. Math could shape the world differently but the way it is taught in schools does not have much impact on everyday life.

— Becca, Bentonville West High School

“To be honest, I don’t see the point in learning all of the complicated math.”

In a realistic point of view, I need to know how to cut a cake or a piece of pie or know how to divide 25,000 dollars into 10 paychecks. On the other hand, I don’t need to know the arc and angle. I need to throw a piece of paper into a trash can. I say this because, in all reality and I know a lot of people say this but it’s true, when are we actually going to need this in our real world lives? Learning complicated math is a waste of precious learning time unless you desire to have a career that requires these studies like becoming an engineer, or a math professor. I think that the fact that schools are still requiring us to learn these types of mathematics is just ignorance from the past generations. I believe that if we have the technology to complete these problems in a few seconds then we should use this technology, but the past generations are salty because they didn’t have these resources so they want to do the same thing they did when they were learning math. So to be honest, I don’t see the point in learning all of the complicated math but I do think it’s necessary to know the basic math.

— Shai, Julia R Masterman, Philadelphia, PA

Learn more about Current Events Conversation here and find all of our posts in this column .

Department of Mathematics

The mathematics major.

This page has a few notes that may be helpful to mathematics majors. Other useful sources of information: 

• For details about math major requirements, please see the current edition of YCPS.
• For more information, take a look at our extensive  Math major FAQ.
• For detailed information about introductory courses and assistance choosing your path through them, please visit our  first year student resources site . 
• A list of recent textbooks for our courses is available. 

In summary: 

The introductory sequence into the mathematics major consists of linear algebra (Math 225 or 226), analysis (Math 255 or 256), and multvariable analysis / calculus (Math 302 or 120). 

Each Mathematics Major must take the senior seminar, Math 480 or Math 481, or the senior essay, Math 475. 

In total, mathematics majors must complete ten mathematics courses numbered 200 or higher (counting the introductory sequence and the senior seminar). 

There are two distributional requirements, categories and core areas.

There are five categories: algebra, combinatorics and number theory; logic and foundations; analysis; geometry and topology; applied mathematics. From three of the five categories, at least two courses in each must be completed. Yale course search provides current listing and descriptions of the courses. It lists the attributes for each course, and can be used to search for courses with a particular attribute. (A sample list of courses that could be offered, by category, can be found below.) 

For the second distributional requirement, students are required to take courses from at least two of the three core areas (all three are recommended): Algebra (Math 350 or higher), Real Analysis (Math 305 or higher) and Complex Analysis (Math 310 or higher). These courses form the core of the undergraduate major. 

The requirements for the Degree of Bachelor of Science in Mathematics include those for the B.A. degree, plus two additional advanced science courses approved by the DUS. A list of approved courses can be found in the  Math major FAQ .

Pure mathematics majors can count up to two courses from related departments. Some of these courses are listed below; a full list can be found in the  Math major FAQ . ( Joint majors may not substitute courses from other departments - a course to be counted toward the math requirements must have a math number - reasons for this policy are explained in our Math major FAQ .) 

Below is a list of courses that tend to belong to each category. Some of these courses are not offered every year, new ones may be added, and our offering may change in other ways in any given year. For a current list of courses that count toward a particular category, with up-to-date prerequisites, we encourage you to use the attribute search on YCS.

Algebra, Combinatorics, and Number Theory

(Math 350 and Math 370 are often taken as a 2-term sequence. Math 380 may also be taken for graduate credit, by students who have a graduate course requirement in the intensive major or the B.S./M.S. program. )

225 or 226 Linear Algebra 

244 Discrete Mathematics

340 Advanced linear algebra

345 Modern Combinatorics

350 Introduction to Abstract Algebra (also carries core area algebra attribute)

353 Introduction to Representation Theory (typically offered every other year)

354 Number Theory

370 Fields and Galois Theory (also carries core area algebra attribute)

373 Algebraic number theory (typically offered every other year)

380 Modern Algebra  (also carries core area algebra attribute)

440 Introduction to Algebraic Geometry (typically offered every other year)

Logic and Foundations

Math 270  Set Theory

Phil 267  Mathematical L ogic   (may count for pure math major only, with limit as noted above)

Phil 427 Computability and Logic (may count for pure math major only, with limit as noted above)

(Math 320-325 and Math 310-315 are generally taken as two term sequences; Math 315, 320, and 325 may also be taken for graduate credit, by students who have a graduate course requirement in the intensive major or the B.S./M.S. program.)

255 or 256 Analysis I

246  Ordinary Differential Equations 

302 Multivariable Analysis

305 Real Analysis (also carries core area real analysis attribute)

310 Introduction to Complex Analysis (also carries core area complex analysis attribute)

315 Intermediate Complex Analysis (also carries core area complex analysis attribute)

320 Measure Theory and Integration (also carries core area real analysis attribute)

325 Introduction to Functional Analysis (also carries core area real analysis attribute)

447 Partial differential equations  (typically offered every other year)

Geometry and Topology

360 Introduction to Lie Groups

430 Introduction to Algebraic Topology  (typically offered every other year)

435 Differential Geometry (typically offered every other year)

544 Introduction to algebraic topology (This is the only graduate course that carries an attribute.)

Applied Mathematics

241  Probability Theory

242  Theory of Statistics

246 Ordinary Differential Equations 

247 Partial Differential Equations

251 Stochastic Processes

310 Complex Analysis

330 Advanced probability

345 Modern combinatorics

421 Mathematics of Data Science (typically offered every other year)

Other courses that may be of interest

As noted above, these only count for pure math majors (not joint-math), and there is a maximum of two that may be counted. They carry no attributes. For the full list of courses that can be counted as outside electives for pure math majors, please see the math major FAQ . 

AMTH 437  Optimization Techniques

CPSC 365 or 366  (Intensive) Algorithms

(and other CPSC classes, such as 267, 427, 440, 460, 468)

ECON 135 or 136 (these may not be counted along with MATH 241 or 242)

ECON 351 Mathematical economics: game theory

S&DS 364 Information theory

S&DS 410 Statistical inference

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Mathematics of Data and Computing Bachelor's Degree

Undergraduate Major

Mathematicians are inquirers and problem solvers. Math seeks to find precise, relevant answers to theoretical as well as real-world questions; for this reason, it is the language of science. Tech companies and research organizations hire mathematicians to tackle challenging problems and support innovation. This program draws from the disciplines of mathematics and computer science to focus on the theoretical and applied aspects of computation, information, logic, and data.

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Why Pursue a Bachelor's Degree in Mathematics of Data and Computing

This bachelor’s degree combines significant coursework in Computer Science and Mathematics. This type of transdisciplinary education prepares students for occupations that demand highly developed analytical problem-solving skills. There are few academic programs of this type in the world.

The Computer Science coursework focuses on data-centric courses such as Data Structures, Analysis of Algorithms, and Database Systems. The Mathematics coursework emphasizes courses that provide the mathematical foundations of computation and data analysis. Examples of key courses include Abstract Algebra, Discrete Mathematics, Cryptography, Logic and Computability, and Probability.

Pathways to Mathematics and Computer Science Professions

Interested in a mathematics or computer science career? UTSA is home to several organizations to help you network and pursue your dream job.

• Association for Computing Machinery
• American Mathematical Society
• Association for Symbolic Logic
• Society of Industrial and Applied Mathematics

Admission Requirements

Scholarships, careers, salary & skills.

When you apply to UTSA, you select the major you'd like to study. The choice of major will not impact if you get admitted to the University ( all students must meet UTSA's general admission requirements ); however, some majors will require additional admission requirements to be able to declare the major your freshman year.

Pro Tip: Even if you don't think you will qualify for financial aid, you should still submit the FAFSA! Information from the FAFSA could impact certain scholarships that are even merit-based.

UTSA Scholarship Hub

Through one general scholarship application, you can automatically be considered for dozens of scholarships at UTSA, including scholarships that are available for this major. In order to access all available scholarship applications on the UTSA Scholarship Hub, you must be an admitted student. If you are a student applying for admission, but have not yet been admitted, you may sign in and complete the Scholarship Hub’s General Application as long as you have authenticated your myUTSA ID and Passphrase. Once you are admitted to UTSA, please sign back in to the Scholarship Hub to see if there are any additional scholarship opportunities available for you to pursue.

UTSA Scholarship Hub College of Sciences Scholarships

Distinguished Scholarship

UTSA offers an automatic merit-based scholarship to incoming new freshman and transfer students who display exceptional scholastic achievement in high school by the priority deadline. Non-resident and international students awarded a Distinguished Scholarship for a minimum of $1,000 for the academic year will be granted a waiver for non-resident tuition if scholarship eligibility is maintained. This means out-of-state and international students could pay in-state tuition! For fall admitted freshmen, this scholarship is valued up to $20,000 for up to four years. For fall or spring admitted transfer students, this scholarship is valued up to $6,000 for up to two years. Renewal eligibility must be maintained and funding must be available.

UTSA Bold Promise

Although not a scholarship, UTSA is committed to cover tuition and mandatory fees 100% for eligible students who come from low and middle-income Texas families.

UTSA prepares you for future careers that are in demand. See possible careers below. This data is pulled by a third-party tool called Emsi, which pulls data from sources like the U.S. Bureau of Labor Statistics, U.S. Census Bureau, online job postings, other government databases and more to give you regional and national career outlook related to this academic program. On top of the resources your college will provide, the University Career Center offers several resources to help students identify and develop the global skills necessary to successfully pursue and achieve lifelong career goals.

Minors & Certificates

After selecting a major area of study and enrolling at UTSA, degree-seeking students can choose from a variety of minors and certificates to supplement their education. Although not required, minors and certificates can help students customize their UTSA experience based on their passions and unique career goals.

Course Offerings

The Mathematics of Data and Computing program combines significant coursework from Computer Science and Mathematics to provide a solid foundation in the field.

Computer Science coursework focuses on data-centric courses such as Data Structures, Analysis of Algorithms, and Database Systems. Mathematics coursework emphasizes courses that provide the mathematical foundations of computation and data analysis. View our flowchart of course options available while pursuing this degree.

The Honors Experience

Realize your full potential at The University of Texas at San Antonio’s Honors College. Rooted in experiential learning, our classes and programs are hands-on, project-based, and customizable to fit your individual goals. Students in any majors can get invited to our Honors College. Turn your passions into marketable skills for the future!

“I love the challenge. There’s always a new problem to be solved. It’s like a puzzle that requires logic and math to solve. It’s always different.”

The College of Sciences is an institutional leader in both teaching and research. Participating in research will help you become an investigative problem-solver and a more competitive graduate. Our world-class faculty will help you sharpen your scientific skills so they can be applied to make tangible, life-changing solutions.

You’ll have access to state-of-the-art facilities like the newly opened 160,349 square foot Science and Engineering Building, the Mesquite Living Laboratory, which houses an outdoor classroom that promotes environmental education, and the School of Data Science, which is located downtown and focuses on training a highly-skilled workforce in the fields of cybersecurity, data analytics, and digital asset management.

Internships allow you to obtain work experience, explore a chosen career path and increase your marketability to employers. Students can access Handshake, UTSA’s jobs portal, to search for jobs and internships and recruiting and event information. UTSA’s Career Center has a COS career counselor who provides internship opportunities and advice to students across every science major.

Student Success

UTSA is all about your success. Our experiential learning initiative takes what you learn in the classroom and helps you apply it to real life. As a student in the College of Sciences (COS) , you will explore, engage and reflect on your experiences to launch your career in a global society. The COS Student Success Center is a one-stop resource to help you achieve your academic, personal and professional goals. Receive tutoring, find internships, connect with industry professionals for job opportunities, and enhance your professional development skills through the center’s comprehensive programming.

MS in Mathematics

The Master of Science in Mathematics provides students with basic graduate training in mathematics. As an MS student, you'll choose from a wide ranging program of study that may focus on pure or applied mathematics. The program's flexible coursework is designed to prepare you for employment in areas such as academia, government, business, industry, or for further graduate study. You'll work with your graduate advisor to design a program of study geared towards your interests and goals.

Please see the  MS Handbook  for additional information about the program.

Program Requirements

• A minimum of 9 courses, a total of at least 30 credits, are required to complete the MS in Mathematics.
• A course must be worth at least 3 credits to count toward the 9 course requirement.
• At least three of the courses must be Math courses numbered above 200.
• All courses must be completed with grades of grades of B- or better to count towards the degree.
• If the 9 courses do not add up to 30 credits, a student may take any Math course above 120, or mathematically-significant related fields course toward the degree to reach the credit limit. Unless otherwise stated, the following courses are excluded from counting towards the course requirements: Math 192, 193, 195-196, 291-292, 294-298. However, these courses may be counted toward the total 30 credit requirement.
• A maximum of two reading courses (Math 293) may be used for the 9 required courses, while only up to 3 credits worth of reading courses may satisfy one of the three 200-level course requirements. All Math 293 courses must be approved prior to the start of the semester they will be completed. The student must request a syllabus from the instructor that is sent to the Graduate Committee for approval.

Course Requirements

The course requirements are broken down into three categories plus a thesis option.

• 3 regularly offered Math courses above 120.
• 1 course must be at the 200 level, not including Math 293 or a Special Topics course.
• Each course must be in a separate discipline, indicated by the 2nd digit of the course numbering.   
• 4 regularly offered Math courses above 120.
• In consultation with the student's adviser and with approval from the graduate committee, students may choose the four courses such that they form a concentration in a sub-discipline of mathematics. This will then be indicated informally on the student's transcript. Concentrations may be as broad as "Computational Mathematics" or "Topology," but also very specific if there are courses to match. Please see the  MS Handbook  for more examples. A student can choose predetermined concentrations, choose their own, or not choose one at all. Students choosing a concentration must email the Graduate Director one month prior to graduation to indicate which concentration they choose, otherwise none will be given.
• Special topics courses in a given area must be approved by the Graduate Committee.  
• 2 courses, which can be any Math course numbered above 100 or "related fields" courses.
• This may include upper level, mathematically significant courses in Computer Science, Physics, Economics, or other departments. Please see the  list of courses  that have already been approved and disapproved in this category. If a course is not listed there, then a student can ask the Graduate Committee to approve it as an elective course.
• Equivalent to 1 concentration course and 1 elective course.
• Satisfies 1 of the 3 200-level overall course requirements.
• A student fulfills this requirement by writing an expository paper on a specific topic in mathematics under the direction of a member of the department, and upon completion, presenting it before a committee of three or more faculty members. Please see  MS Handbook  for more details.
• Students  must  enroll in courses Math 295 and 296 in their  final year of study , which account for 5 credits each toward the 30 credits, but not toward the 7 other total courses needed.

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From High School to College Calculus: Beliefs about Sense-Making and Mistakes

• Research Article
• Published: 06 October 2020
• Volume 4 , pages 73–94, ( 2021 )

Cite this article

• Terrie M. Galanti   ORCID: orcid.org/0000-0003-2948-7898 1 &
• Angela D. Miller   ORCID: orcid.org/0000-0001-9737-6634 2  

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Despite longstanding efforts in the K-12 STEM education community to create meaningful mathematical experiences across disciplines, mathematics continues to be a siloed subject which is tracked based on ability. With an increasing number of high-achieving students enrolling in Algebra I in Grade 7 or earlier, there is a need for research on the readiness of accelerated STEM-intending students to persist in mathematics at the college level. A mathematical mindset framework was employed to explore the relationships between level of Algebra I acceleration, student ( n  = 2111) and instructor ( n  = 141) beliefs about sense-making and mistake-making, and attitudes in first-semester college calculus. Findings from a series of multilevel analyses indicate that interactions between student mathematical mindset and perceived progressive teaching practices influence attitudes toward mathematics. While student-centered instruction had a slightly negative effect on attitude, there was a differential effect in relation to student beliefs about sense-making as a metric of success in mathematics. These findings contribute to empirical understandings of mathematical mindset and the complex transition from high school calculus to college calculus. Implications for interdisciplinary STEM education and persistence in STEM undergraduate study are discussed.

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What College Freshmen Believe About Themselves: An Investigation of Mathematical Mindset, Identity, Self-Efficacy, and Use of Self-Regulated Learning Strategies in Mathematics

“this is the first time i’ve done this”: exploring secondary prospective mathematics teachers’ noticing of students’ mathematical thinking.

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Galanti, T.M., Miller, A.D. From High School to College Calculus: Beliefs about Sense-Making and Mistakes. Journal for STEM Educ Res 4 , 73–94 (2021). https://doi.org/10.1007/s41979-020-00039-7

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Mathematicians and Statisticians

Mathematicians and statisticians analyze data and apply computational techniques to solve problems.

Mathematicians and statisticians typically do the following:

• Decide what data are needed to answer specific questions or problems
• Apply mathematical theories and techniques to solve practical problems in business, engineering, the sciences, and other fields
• Design surveys, experiments, or opinion polls to collect data 
• Develop mathematical or statistical models to analyze data
• Interpret data and communicate analyses to technical and nontechnical audiences
• Use statistical software to analyze data and create visualizations to aid decision making in business

To solve problems, mathematicians rely on statisticians to design surveys, questionnaires, experiments, and opinion polls for collecting the data they need. For most surveys and opinion polls, statisticians gather data from some people in a particular group. Statisticians determine the type and size of this sample for collecting data in the survey or poll.

Following data collection is analysis, which involves mathematicians and statisticians using specialized statistical software. In their analyses, mathematicians and statisticians identify trends and relationships within the data. They also conduct tests to determine the data’s validity and to account for possible errors. Some help write software code to analyze data more accurately and efficiently.

Mathematicians and statisticians present findings from their analyses and discuss the data’s limitations in order to ensure accurate interpretation. They may present written reports, tables, and charts to team members, clients, and other users.

Mathematicians and statisticians work in any field that benefits from data analysis, including education, government, healthcare, and research and development.

Colleges and universities.  Mathematicians and statisticians working in postsecondary schools may study theoretical or abstract concepts in these fields. They identify, research, and work to resolve unexplained issues in mathematics and explore mathematical or statistical theories to increase knowledge and understanding about the field.

Government.  Mathematicians and statisticians working in government develop surveys and collect and analyze data on a variety of topics, including employment, crop production, and energy use. At all levels of government, these data help to inform policy proposals and decisions that affect the public.

Healthcare .  Statisticians known as biostatisticians or biometricians work in pharmaceutical companies, public health agencies, or hospitals. They may design studies to test whether drugs successfully treat diseases or medical conditions. They may also help identify the sources of outbreaks of illnesses in humans and animals.

Research and development .  Mathematicians and statisticians design experiments for product testing and development. For example, they may help design experiments to see how car engines perform when exposed to extreme weather or analyze consumer data for use in developing marketing strategies. 

Typically, mathematicians and statisticians work on teams with other specialists to solve problems. For example, they may work with chemists, materials scientists, and chemical engineers to analyze the effectiveness of a new drug or help data scientists develop statistical models.

Mathematicians held about 2,000 jobs in 2021. The largest employers of mathematicians were as follows:

Statisticians held about 34,200 jobs in 2021. The largest employers of statisticians were as follows:

Mathematicians and statisticians typically work in offices. They also may work on teams with engineers, scientists, and other specialists.

Work Schedules

Most mathematicians and statisticians work full time. Deadlines and last-minute requests for data or analysis may require overtime. In addition, these workers may travel to attend seminars and conferences.

Mathematicians and statisticians typically need at least a master’s degree in mathematics or statistics. However, some positions are available to those with a bachelor’s degree.

Students who are interested in becoming mathematicians or statisticians should take as many math courses as possible in high school.

For jobs with the federal government, candidates need at least a bachelor’s degree or significant coursework in mathematics. In private industry, mathematicians typically need either a master’s or a doctoral degree; statisticians typically need a master's degree, but some entry-level positions may accept candidates with a bachelor's degree.

Most colleges and universities have bachelor’s degree programs in mathematics. Courses usually include calculus, differential equations, and linear and abstract algebra. Mathematics students also commonly take courses in a related field, such as computer science, physics, or statistics.

Many universities offer master’s and doctoral degrees in theoretical or applied mathematics. Students who get a doctoral degree may work as professors of mathematics in a college or university.

Statisticians typically need a master’s degree, but some entry-level positions may accept candidates with a bachelor’s degree.

Students majoring in statistics also may take courses in another field, such as computer science, life sciences, or physical sciences. These courses may help prepare students to work in a variety of industries. For example, coursework in biology, chemistry, or health sciences is useful for testing pharmaceutical or agricultural products. Physics may be useful for statisticians working in manufacturing on quality improvement.

Advancement

Mathematicians and statisticians may advance to become senior mathematicians or statisticians or to work in other managerial roles. A master’s or doctoral degree may be required for some advancement opportunities.

Statisticians typically have an interest in the Thinking and Organizing interest areas, according to the Holland Code framework. The Thinking interest area indicates a focus on researching, investigating, and increasing the understanding of natural laws. The Organizing interest area indicates a focus on working with information and processes to keep things arranged in orderly systems.

If you are not sure whether you have a Thinking or Organizing interest which might fit with a career as a statistician, you can take a career test to measure your interests.

Statisticians should also possess the following specific qualities:

Critical-thinking skills. Statisticians use logic and reasoning to identify the strengths and weaknesses of alternative solutions, conclusions, or approaches to problems.

Math skills. Statisticians use statistics, calculus and linear algebra to develop their models and analyses.

Problem-solving skills . Statisticians must develop techniques to overcome problems in data collection and analysis, such as high nonresponse rates, so that they can draw meaningful conclusions.

Speaking skills. Because statisticians often work in teams, they must be able to present statistical information and ideas so that others will understand.

Writing skills. Good writing skills are important for statisticians because they write reports explaining technical matters to persons without their level of statistical expertise.

The median annual wage for mathematicians was $108,100 in May 2021. The median wage is the wage at which half the workers in an occupation earned more than that amount and half earned less. The lowest 10 percent earned less than $61,760, and the highest 10 percent earned more than $169,500.

The median annual wage for statisticians was $95,570 in May 2021. The lowest 10 percent earned less than $49,350, and the highest 10 percent earned more than $157,300.

In May 2021, the median annual wages for mathematicians in the top industries in which they worked were as follows:

In May 2021, the median annual wages for statisticians in the top industries in which they worked were as follows:

Overall employment of mathematicians and statisticians is projected to grow 31 percent from 2021 to 2031, much faster than the average for all occupations.

About 4,100 openings for mathematicians and statisticians are projected each year, on average, over the decade. Many of those openings are expected to result from the need to replace workers who transfer to different occupations or exit the labor force, such as to retire. 

Projected employment of mathematicians and statisticians varies by occupation (see table). Employment growth for statisticians is expected to result from more widespread use of statistical analysis to inform business, healthcare, and policy decisions. The amount of digitally stored data will increase over the projections decade as people and companies continue to conduct business online and use social media, smartphones, and other mobile devices. As a result, businesses will increasingly need statisticians to analyze the large amount of information and data collected. Statistical analyses will help companies improve their business processes, design and develop new products, and advertise products to potential customers.

For more information about mathematicians, including training, especially for doctoral-level employment, visit

American Mathematical Society

For more information about statisticians, visit

American Statistical Association

This is Statistics

For specific information on careers in applied mathematics, visit

Society for Industrial and Applied Mathematics

For information on federal government requirements for mathematician positions, visit

U.S. Office of Personnel Management

Where does this information come from?

The career information above is taken from the Bureau of Labor Statistics Occupational Outlook Handbook . This excellent resource for occupational data is published by the U.S. Department of Labor every two years. Truity periodically updates our site with information from the BLS database.

I would like to cite this page for a report. Who is the author?

There is no published author for this page. Please use citation guidelines for webpages without an author available. 

I think I have found an error or inaccurate information on this page. Who should I contact?

This information is taken directly from the Occupational Outlook Handbook published by the US Bureau of Labor Statistics. Truity does not editorialize the information, including changing information that our readers believe is inaccurate, because we consider the BLS to be the authority on occupational information. However, if you would like to correct a typo or other technical error, you can reach us at [email protected] .

I am not sure if this career is right for me. How can I decide?

There are many excellent tools available that will allow you to measure your interests, profile your personality, and match these traits with appropriate careers. On this site, you can take the Career Personality Profiler assessment, the Holland Code assessment, or the Photo Career Quiz .

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In the College of Arts and Sciences   .

Course Offerings    

Mathematics is the language of modern science; basic training in the discipline is essential for those who want to understand, as well as for those who want to take part in, the important scientific developments of our time. Acquaintance with mathematics is also extremely useful for students in the social sciences and valuable for anyone interested in the full range of human culture and the ways of knowing the universe in which we live.

The Department of Mathematics faculty has strong and broad groups specializing in algebra, number theory, combinatorics, real and complex analysis, Lie groups, topology and geometry, logic, probability and statistics, mathematical physics, and applied mathematics. Additionally, several other departments at Cornell offer courses which involve a significant amount of advanced mathematical content.  These include computer science, economics, operations research, physics, and statistics. Certain courses in these and other disciplines can be readily integrated into the math major though the various concentrations which are offered.

The department offers a rich variety of undergraduate courses. Additionally, some of the introductory graduate courses are suitable for undergraduates who have completed a rigorous foundation of 4000-level coursework in mathematics. Under some conditions, a student may carry out an independent reading or research project for college credit under the supervision of a faculty member.

Members of the department are available to discuss with students the appropriate course for their levels of ability and interest, and students are urged to avail themselves of this help. Students who want to take any of the courses numbered 3000 or above are invited to confer with the instructor before enrolling.

Website: math.cornell.edu

T. Holm, chair; X. Cao, director of undergraduate studies; I. Peeva, director of graduate studies; M. Aguiar, D. Barbasch, Y. Berest, R. Connelly, K. Delp, B. Dozier, D. Freund, R. Griffiths, D. Halpern-Leistner, T. Healey, J. Hubbard, M. Huntley, S. Jeong, M. Kassabov, A. Knutson, L. Levine, Y. Luo, M. MacDonald, K. Mann, J. Manning, L. Mazurowski, K. Meszaros, M. Mirek, J. Moore, C. Muscalu, A. Nerode, M. Nussbaum, K. Pohland, M. Poór, R. Ramakrishna, R. Ramkumar, T. Riley, L. Saloff-Coste, R. Sjamaar, S. Solecki, P. Sosoe, B. Speh, D. Stern, M.E. Stillman, S. Strogatz, E. Swartz, N. Templier, A. Townsend, A. Vladimirsky, M. Wegkamp, J. West, Y. Yang, I. Zakharevich, X. Zhou, D. Zywina

Advanced Placement and Transfer Credit:

Students who have had some calculus should carefully read “ Advanced Placement   ,” and those who have not taken an advanced placement exam should take a placement test at Cornell during fall or spring orientation.

The linear algebra and multivariable calculus courses that we offer ( MATH 2210   , MATH 2220   , MATH 1920   , and MATH 2940   ) cover considerably more material and in considerably greater depth than that which is covered in high school courses in these subjects. Students who have completed coursework in linear algebra and/or multivariable calculus and have a strong interest in challenging theoretical mathematics may consider enrolling in MATH 2230   – MATH 2240   . College courses may be eligible for transfer credit. Students who have completed a rigorous course in multivariable calculus that is not transferable may take the Engineering Math Advanced Standing Exam. There is no placement test for linear algebra, and it should be noted that 4000-level linear algebra courses are generally not regarded as meeting the prerequisites for the math major or minor.

Visit the Math Department web site for more information on advanced placement , including dates, times, and locations for Cornell math placement exams, and guidelines for transferring credit from another institution .

Course Selection Guidance:

For guidance in selecting an appropriate course, including how to factor advanced placement or transfer credit into that decision, please consult First Steps in Math . New students will have an opportunity to ask questions about math placement during fall orientation at the Arts & Sciences Open House; however, it should be noted that the Cornell placement tests are often held before the open house. Students who are unsure if they need a calculus placement test should ask the director of undergraduate studies for advice in advance of the exam.

Precalculus:

Students who need to take Calculus I ( MATH 1106    or MATH 1110   ) but are lacking the necessary prerequisites may take MATH 1101    to prepare. Courses labeled “college algebra” or “precalculus” at other universities, while not eligible for transfer credit to Cornell, may be used to satisfy the prerequisites for Calculus I.

Calculus and Linear Algebra:

Students should consult their advisors and keep major prerequisites in mind when planning a suitable program. The following are general recommendations. Consult First Steps in Math for more detail. The director of undergraduate studies will gladly meet with students to offer further advice.

• Students who expect to major in mathematics should take MATH 1110   – MATH 1120    and continue with MATH 2210   – MATH 2220   . This sequence is also a good choice for those studying economics or a science for which a strong math background is recommended. Students with a 5 on the Calculus BC exam and a strong interest in challenging theoretical mathematics may consider MATH 2230   – MATH 2240   , especially if they have had some prior exposure to linear algebra and multivariable calculus.
• MATH 1910   – MATH 1920   – MATH 2930   – MATH 2940    is the core sequence for engineering students. It is also recommended by some advisors in fields strongly related to the mathematical and physical sciences, such as astronomy, computer science, physics, and physical chemistry. MATH 1910    assumes students have already taken a good first course in calculus, which can be satisfied with a 5 on the Calculus AB exam or a course like MATH 1110   . Students in this sequence who plan to take more math should consider a 3000-level course to gain experience with proofs before attempting a 4000-level course.
• MATH 1110   – MATH 1120    followed by MATH 2130    or MATH 2310    is a good choice for students who need to master the basic techniques of calculus but whose majors will not require a substantial amount of mathematics. MATH 1110   – MATH 2310    is an option for students who need some linear algebra but not a full year of calculus.
• MATH 1106    is an option for students whose major requires only one semester of calculus.  Some topics are covered in less depth than in MATH 1110   , while more advanced topics are introduced. MATH 1106    focuses on modeling using examples from the life sciences. It introduces some fundamental concepts of calculus and provides a brief introduction to differential equations. Students who may take more than one semester of calculus should take MATH 1110    rather than MATH 1106   .
• Students who are undecided about their future studies at Cornell but think they may involve a substantial amount of math can keep their options open by taking Calculus I ( MATH 1110    or AP credit), Calculus II ( MATH 1120    or AP credit), and Linear Algebra ( MATH 2210   ). Multivariable Calculus ( MATH 2220   ) would be the next step for students who are still leaning in the direction of a math-related major and may wish to take more advanced mathematics.

Some switching between sequences (1) and (2) is possible provided classes are taken in the right order. For example,  MATH 2220    must be preceded by a semester of linear algebra. In general,  MATH 2130    and  MATH 2310    are not the best preparation for further study in mathematics. Students who have taken these courses should consult the director of undergraduate studies for advice before continuing.

Special-Purpose Sequences:

Students who will take no more than two semesters of mathematics can gain a broader view of the subject by taking one semester of calculus and one non-calculus mathematics course. The following options are particularly useful for students in the life and social sciences and will satisfy the mathematics requirement for most medical schools.

• MATH 1105   – MATH 1106    provides a one-year introduction to the mathematical topics that are most useful to biologists and social scientists. ( MATH 1110    may be substituted for MATH 1106   .)
• An introductory statistics course ( MATH 1710   , for example), taken before or after a semester of calculus ( MATH 1106    or MATH 1110   ), teaches students how to work with data and can be more useful in some disciplines than a second semester of calculus.

Students who want two semesters of calculus are advised to take the first two semesters of one of the calculus sequences, but students with excellent performance in MATH 1106    may follow that course with MATH 1120   .

Minor in Mathematics:

The mathematics minor is available to undergraduates majoring in other disciplines across the university who have an interest in studying mathematics. Students planning a minor in mathematics may seek advice on course selection from the director of undergraduate studies . Information is also available at math.cornell.edu/minor , including how to apply for the minor.

Student Grade Option

Courses must be taken for a letter grade in order to count toward admission to the math minor or to satisfy any math minor requirement. This requirement is waived for all classes taken in spring 2020, and an “S” grade will be accepted regardless of the usual minimum grade requirements.

Transfer Credit

Courses taken at another institution may be used to satisfy the math minor prerequisites and to replace at most one course toward the minor requirements. These courses must be approved for transfer credit and appear on the Cornell transcript with Cornell course equivalents.

Visit the Math Department web site for more information about transferring credit from another institution .

Prerequisites:

Students are admitted to the minor after successfully completing a semester of linear algebra — MATH 2210   , MATH 2230   , or MATH 2940    with a grade of B– or better — and a semester of  multivariable calculus — MATH 2220   , MATH 2240   , or MATH 1920    with a grade of B– or better. The department recommends MATH 2210   – MATH 2220    or MATH 2230   – MATH 2240   . MATH 2130    and MATH 2310    are not recommended for students planning a math minor; however, MATH 2130    with a grade of B+ or better may be accepted as a substitute for MATH 2220   , and MATH 2310    with a grade of B+ or better may be accepted as a substitute for MATH 2210   .

Credit for  MATH 1920    may be obtained by passing a placement exam during orientation; however, a score equivalent to a B- or better is required to satisfy the prerequisite for the math minor. Students who score below a B- and wish to join the minor may not attempt the exam a second time but should instead enroll in a multivariable calculus course.

Students who receive below the minimum grade in one of these prerequisite courses should contact the undergraduate coordinator immediately.

Requirements:

Students must complete four 3000- or 4000-level MATH courses. Only courses with a MATH prefix or cross-listed as such are allowed; no substitutions. At least one course must be in algebra and one in analysis. Eligible algebra and analysis courses are the same as those listed for the math major requirements (1) and (2) below. At least one of the four courses must be at the 4000-level or above. A course may be counted toward the minor only if it is taken for a letter grade and a grade of C– or better is received for the course.

Major in Mathematics:

The mathematics major adapts to a number of purposes. It can emphasize the theoretical or the applied. It can be appropriate for professionals and nonprofessionals alike, and can be broad or narrow. It can also be combined easily with serious study in another subject in the physical, biological, or social sciences by means of a double major and/or concentration. (See “ Double Majors ” below for more information.)

Questions concerning the major should be brought to the undergraduate coordinator. Information is also available at math.cornell.edu/major , including how to apply for the major.

Note: In addition to the major requirements outlined below, all students must meet the college graduation requirements   . 

Courses must be taken for a letter grade in order to count toward admission to the math major or to satisfy any math major requirement. This requirement is waived for all classes taken in spring 2020, including courses taken for an outside concentration, and an “S” grade will be accepted regardless of the usual minimum grade requirements.

Courses taken at another institution may be used to satisfy the math major prerequisites and to replace at most two courses toward the major requirements. These courses must be approved for transfer credit and appear on the Cornell transcript with Cornell course equivalents.

Students are admitted to the major after successfully completing a semester of linear algebra — MATH 2210   , MATH 2230   , or MATH 2940    with a grade of B– or better — and a semester of  multivariable calculus — MATH 2220   , MATH 2240   , or MATH 1920    with a grade of B– or better. The department recommends MATH 2210   – MATH 2220    or MATH 2230   – MATH 2240   . MATH 2130    and MATH 2310    are not recommended for students planning a math major; however, MATH 2130    with a grade of B+ or better may be accepted as a substitute for MATH 2220   , and MATH 2310    with a grade of B+ or better may be accepted as a substitute for MATH 2210   . A 3- or 4-credit computer programming course is also required with a letter grade of C– or better. Eligible courses include: CS 1110   , CS 1112   , CS 2110   , and CS 2112   .

Credit for  MATH 1920    may be obtained by passing a placement exam during orientation; however, a score equivalent to a B- or better is required to satisfy the prerequisite for the math major. Students who score below a B- and wish to join the major may not attempt the exam a second time but should instead enroll in a multivariable calculus course.

Students who have taken a course in linear algebra and/or multivariable calculus during high school should consider taking MATH 2230   – MATH 2240   .  This sequence gives a more abstract, proof-oriented treatment of the material. Students with an advanced background in linear algebra and/or multivariable calculus should contact the undergraduate coordinator for advice as soon as possible. Note that 4000-level linear algebra courses are generally not regarded as meeting the prerequisites for the math major.

Students who receive below the minimum grade in one of these prerequisite courses should contact the undergraduate coordinator immediately. Any repeated attempt to fulfill a math major prerequisite requires pre-approval from the math majors committee.

The minimum number of required credits to complete the major is 27. However, typical students accrue between 32 and 36 credits.

Students must complete nine courses, as described in items 1–3 below, under the following constraints:

• At least 5 courses with a MATH prefix numbered 3000 or above must appear on the student’s transcript. (Double majors enrolling in cross-listed courses should pay particular attention to this constraint.)
• At least two of the MATH courses taken must be at the 4000-level (or above).
• A course may be counted toward the major only if it is taken for a letter grade and a grade of C– or better is received for the course.
• No course may be used to satisfy more than one requirement for the major.
• 2-credit courses count as half courses.
• MATH courses numbered between 4980 and 5999 do not count toward the major.

Major advisors may make adjustments to the major requirements upon request from an advisee, provided the intent of the requirements is met. In particular, many suitable graduate courses are not listed here, but are available for undergraduates who are well prepared.

1. Two courses in algebra:

Eligible courses are:

• MATH 3320 - Introduction to Number Theory
• MATH 3340 - Abstract Algebra
• MATH 3360 - Applicable Algebra
• MATH 4310 - Linear Algebra
• MATH 4330 - Honors Linear Algebra
• MATH 4340 - Honors Introduction to Algebra
• MATH 4370 - Computational Algebra
• MATH 4500 - Matrix Groups
• MATH 4560 - [Geometry of Discrete Groups]

2. Two courses in analysis:

• MATH 3110 - Introduction to Analysis
• MATH 3210 - Manifolds and Differential Forms
• MATH 3270 - Introduction to Ordinary Differential Equations
• MATH 4130 - Honors Introduction to Analysis I
• MATH 4140 - Honors Introduction to Analysis II
• MATH 4180 - Complex Analysis
• MATH 4200 - Differential Equations and Dynamical Systems
• MATH 4210 - Nonlinear Dynamics and Chaos
• MATH 4220 - Applied Complex Analysis
• MATH 4250 - Numerical Analysis and Differential Equations (crosslisted)
• MATH 4260 - Numerical Analysis: Linear and Nonlinear Problems (crosslisted)
• MATH 4280 - Introduction to Partial Differential Equations

3. Five further high-level mathematical courses:

A. concentration in mathematics:, i. four additional math courses numbered 3000 or above:.

At least one of the four courses must be among the geometry/topology courses. Eligible courses include:

• MATH 4520 - Classical Geometries and Modern Applications
• MATH 4530 - Introduction to Topology
• MATH 4540 - Introduction to Differential Geometry
• MATH 4550 - [Applicable Geometry]

MATH 3210    is eligible only if not used for the analysis requirement; MATH 4500    and MATH 4560    are eligible only if not used toward the algebra requirement.

ii. One course dealing with mathematical models:

Eligible courses include  MATH 3610    and any course from outside mathematics with serious mathematical content that deals with scientific matters. Serious mathematical content includes, but is not limited to, extensive use of calculus or linear algebra. Any course from another department that would satisfy one of the concentrations may be used, as well as:

• CS 2110 - Object-Oriented Programming and Data Structures (crosslisted)
• PHYS 1116 - Physics I: Mechanics and Special Relativity
• PHYS 2208 - Fundamentals of Physics II
• PHYS 2213 - Physics II: Electromagnetism
• PHYS 2217 - Physics II: Electricity and Magnetism (crosslisted)

Other 1000-level physics courses and PHYS 2207    may not be used, but some courses in other fields may be accepted. AP credit may not be used.

b. Concentration in Applied Mathematics:

Five additional courses from (iii) and (iv) below, of which at least three are from (iii) and one is from (iv). Of the 9 courses used to fulfill requirements (1), (2), (3 iii), and (3 iv) of the math major with an applied mathematics concentration, at least one course must be taken from three of the four Groups A, B, C, and D below. Non-MATH courses in these groups may be used toward the math modeling requirement (3 iv).

iii. MATH courses numbered 3000 or above:

Iv. courses dealing with mathematical models:.

Eligible courses include  MATH 3610    and any course outside mathematics with serious mathematical content that deals with scientific matters.  Serious mathematical content includes, but is not limited to, extensive use of calculus or linear algebra. Any course from another department that would satisfy one of the concentrations may be used. At most one of the following may be used:

• CS 2110 - Object-Oriented Programming and Data Structures     
• PHYS 1116 - Physics I: Mechanics and Special Relativity    
• PHYS 2208 - Fundamentals of Physics II    
• PHYS 2213 - Physics II: Electromagnetism    
• PHYS 2217 - Physics II: Electricity and Magnetism    

Other 1000-level physics courses and  PHYS 2207    may not be used, but some courses in other fields may be accepted.  AP credit may not be used.

Group A. Differential equations

• MATH 3270 - Introduction to Ordinary Differential Equations  
• MATH 4200 - Differential Equations and Dynamical Systems    
• MATH 4210 - Nonlinear Dynamics and Chaos    
• MATH 4280 - Introduction to Partial Differential Equations    

Group B. Discrete mathematics and combinatorics

• MATH 3360 - Applicable Algebra    
• MATH 4370 - Computational Algebra    
• MATH 4410 - Introduction to Combinatorics I    
• MATH 4420 - Introduction to Combinatorics II    
• MATH 4550 - [Applicable Geometry]    
• CS 4820 - Introduction to Analysis of Algorithms    
• ECON 4020 - [Game Theory I]    
• ECON 4022 - [Game Theory II]    
• ORIE 3300 - Optimization I    
• ORIE 4350 - Introduction to Game Theory    

Group C. Numerical and computational methods

• MATH 4250 - Numerical Analysis and Differential Equations    
• MATH 4260 - Numerical Analysis: Linear and Nonlinear Problems     
• CS 4620 - Introduction to Computer Graphics    
• CS 4670 - Introduction to Computer Vision     
• MAE 4700 - Finite Element Analysis for Mechanical and Aerospace Design    

Group D. Probability and statistics

• MATH 4710 - Basic Probability    
• MATH 4720 - Statistics    
• MATH 4740 - Stochastic Processes    
• ECON 3130 - Statistics and Probability    
• ECON 4130 - Statistical Decision Theory    
• ORIE 3500 - Engineering Probability and Statistics II    
• STSCI 3080 - Probability Models and Inference    
• STSCI 3100 - Statistical Sampling    
• STSCI 4030 - Linear Models with Matrices    

c. Concentration in Computer Science:

Five additional courses from (v) and (vi) below, of which at least one is from (v) and three are from (vi).

v. MATH courses numbered 3000 or above:

Vi. computer science courses with significant mathematical content:.

• CS 3220 - [Computational Mathematics for Computer Science]
• CS 4110 - [Programming Languages and Logics]
• CS 4160 - [Formal Verification]
• CS 4210 - Numerical Analysis and Differential Equations (crosslisted)
• CS 4220 - Numerical Analysis: Linear and Nonlinear Problems (crosslisted)
• CS 4620 - Introduction to Computer Graphics
• CS 4670 - Introduction to Computer Vision
• CS 4700 - Foundations of Artificial Intelligence
• CS 4740 - Natural Language Processing (crosslisted)
• CS 4744 - Computational Linguistics I (crosslisted)
• CS 4775 - Computational Genetics and Genomics (crosslisted)
• CS 4780 - Introduction to Machine Learning
• CS 4783 - Mathematical Foundations of Machine Learning
• CS 4786 - [Machine Learning for Data Science]
• CS 4787 - Principles of Large-Scale Machine Learning Systems
• CS 4789 - Introduction to Reinforcement Learning
• CS 4810 - [Introduction to Theory of Computing]
• CS 4812 - Quantum Information Processing (crosslisted)
• CS 4814 - Introduction to Computational Complexity
• CS 4820 - Introduction to Analysis of Algorithms
• CS 4830 - Introduction to Cryptography
• CS 4850 - [Mathematical Foundations for the Information Age]
• CS 4852 - Networks II: Market Design (crosslisted)
• CS 4860 - Applied Logic (crosslisted)

There are also many CS graduate courses with significant mathematical content that may be used. Interested students should discuss these options with their math faculty advisor (after being admitted to the math major).  

d. Concentration in Economics:

Five additional courses from (vii), (viii), and (ix) below, as follows: one course from (vii), three courses from (viii), and a fifth course from any of (vii), (viii), or (ix).

vii. MATH courses numbered 3000 or above:

Viii. economics courses with significant mathematical content:.

• ECON 3130 - Statistics and Probability or
• ECON 6190 - Econometrics I
• ECON 3140 - Econometrics or
• ECON 6200 - Econometrics II
• ECON 3810 - [Decision Theory I]
• ECON 3825 - Networks II: Market Design (crosslisted)
• ECON 4020 - [Game Theory I]
• ECON 4022 - [Game Theory II]
• ECON 4110 - Cross Section and Panel Econometrics
• ECON 4130 - Statistical Decision Theory
• ECON 4907 - The Economics of Asymmetric Information and Contracts
• ECON 6090 - Microeconomic Theory I
• ECON 6100 - Microeconomic Theory II
• ECON 6130 - Macroeconomics I
• ECON 6140 - Macroeconomics II

Undergraduate enrollment in ECON graduate courses requires permission of instructor.

ix. Courses in operations research with significant mathematical content and dealing with material of interest in economics:

• ORIE 3300 - Optimization I
• ORIE 3310 - Optimization II
• ORIE 4350 - Introduction to Game Theory
• ORIE 4580 - Simulation Modeling and Analysis
• ORIE 4600 - Introduction to Financial Engineering
• ORIE 4740 - Statistical Data Mining I
• ORIE 4741 - Learning with Big Messy Data
• ORIE 5600 - Financial Engineering with Stochastic Calculus I
• ORIE 5610 - Financial Engineering with Stochastic Calculus II

e. Concentration in Mathematical Biology:

Five additional courses from (x) and (xi) below, with three courses from (x) and two courses from (xi).

x. Biology courses that have mathematical content and provide background necessary for work at the interface between biology and mathematics:

• BIOEE 3620 - Dynamic Models in Biology (crosslisted)
• BIONB 4220 - [Modeling Behavioral Evolution]
• BME 3110 - Cellular Systems Biology
• BTRY 3080 - Probability Models and Inference (crosslisted)
• BTRY 4090 - Theory of Statistics (crosslisted)
• BIOCB 4830 - Quantitative Genomics and Genetics
• NTRES 4120 - Wildlife Population Analysis: Techniques and Models

xi. MATH courses numbered 3000 or above:

Particularly appropriate are:

• MATH 4710 - Basic Probability

f. Concentration in Mathematical Physics:

Five additional courses from (xii) and (xiii) below, of which at least one is from (xii) and three are from (xiii).

xii. MATH courses numbered 3000 or above:

Xiii. physics courses that make significant use of advanced mathematics:.

• PHYS 3316 - Basics of Quantum Mechanics
• PHYS 3317 - Applications of Quantum Mechanics
• PHYS 3318 - Analytical Mechanics
• PHYS 3327 - Advanced Electricity and Magnetism
• PHYS 4230 - Statistical Thermodynamics (crosslisted)
• PHYS 4443 - Intermediate Quantum Mechanics
• PHYS 4444 - Introduction to Particle Physics
• PHYS 4445 - Introduction to General Relativity (crosslisted)
• PHYS 4454 - Introductory Solid State Physics (crosslisted)
• PHYS 4481 - Quantum Information Processing (crosslisted)
• PHYS 4488 - Statistical Mechanics
• AEP 4340 - Fluid and Continuum Mechanics
• AEP 4400 - [Nonlinear and Quantum Optics]

g. Concentration in Operations Research:

Five additional courses from (xiv) and (xv) below, of which at least one is from (xiv) and three are from (xv).

xiv. MATH courses numbered 3000 or above:

Xv. courses in operations research in which the primary focus involves mathematical techniques:.

• ORIE 3500 - Engineering Probability and Statistics II
• ORIE 3510 - Introduction to Engineering Stochastic Processes I (crosslisted)
• ORIE 4630 - Operations Research Tools for Financial Engineering (crosslisted)
• ORIE 5640 - Statistics for Financial Engineering (crosslisted)

h. Concentration in Statistics:

Five additional courses from (xvi), (xvii), and (xviii) below. No substitutions are allowed for MATH 4710    or MATH 4720   . Students who have already taken a course with overlapping content should contact the undergraduate coordinator . (For students who have not had experience with real-world data, MATH 1710    is recommended before or concurrent with MATH 4710   . It will not, however, count toward any of the math major requirements.)

• MATH 4720 - Statistics

xvii. One additional MATH course numbered 3000 or above:

Xviii. two courses in other departments with significant content in statistics, complementing (xvii):.

• ECON 3140 - Econometrics
• STSCI 3100 - Statistical Sampling (crosslisted)
• STSCI 3510 - Introduction to Engineering Stochastic Processes I (crosslisted)
• STSCI 4030 - Linear Models with Matrices (crosslisted)
• STSCI 4060 - Python Programming and its Applications in Statistics
• STSCI 4100 - Multivariate Analysis (crosslisted)
• STSCI 4110 - Categorical Data (crosslisted)
• STSCI 4140 - Applied Design (crosslisted)
• STSCI 4520 - Statistical Computing
• STSCI 4550 - Applied Time Series Analysis (crosslisted)
• STSCI 4740 - Data Mining and Machine Learning
• STSCI 4780 - Bayesian Data Analysis: Principles and Practice

STSCI 3510   / ORIE 3510    may not be counted toward (xviii) if MATH 4740    is used for (xvii). At most one regression course ( ECON 3140    or STSCI 4030   / BTRY 4030   ) is allowed for (xviii). At most one of CS 4780   , CS 4786   , ORIE 4740   , or STSCI 4740    is allowed for (xviii).

Double Majors:

A double major with computer science, economics, or physics can be facilitated by the corresponding concentrations described above. The Departments of Computer Science and Economics permit double majors to use courses in the corresponding concentrations to satisfy the requirements of both majors.

Double majors with physics may count eligible physics courses toward both the physics major and the math major’s math physics concentration; however, the Physics Department will not approve courses for an outside concentration if they are being used toward another major or minor.

When enrolling in cross-listed courses, double majors must take care that at least 5 courses with a MATH prefix numbered 3000 or above will appear on their transcript. Students should consult other major departments about any further conditions they may have.

Senior Thesis:

A senior thesis can form a valuable part of a student’s experience in the mathematics major. It is intended to allow students to conduct an in-depth investigation not possible in regular course work. The work should be independent and creative. It can involve the solution of a serious mathematics problem, or it can be an expository work, or variants of these. Conducting independent research, paying careful attention to exposition in the finished written product, and the delivery of an optional oral presentation can have a lasting positive impact on a student’s educational and professional future.

Graduate Courses:

Some exceptional undergraduates, upon completing a rigorous foundation of 4000-level math courses, may wish to further develop their understanding of the material in subsequent graduate courses that the math department offers. The core courses from the mathematics graduate program — MATH 6110   , MATH 6120   , MATH 6310   , MATH 6320   , MATH 6510   , and MATH 6520    — represent a good first exposure to graduate-level mathematics. MATH 6150   , MATH 6160   , MATH 6210   , MATH 6220   , MATH 6710   , and MATH 6720    cover some additional material in a manner suitable to advanced undergraduates.

Undergraduates taking graduate courses should have completed advanced undergraduate courses on the same topic with a grade of A– or better. Interested students should discuss the possibility of taking graduate courses with their faculty advisor in the Math Department prior to enrolling in the course.

The Department of Mathematics awards honors ( cum laude ) and high honors ( magna cum laude and summa cum laude ) to graduating mathematics majors who have performed outstandingly in the major program.

The awards are determined by the Mathematics Major Committee in the latter part of the semester before graduation. The committee will primarily be looking for excellent performance in mathematics courses, particularly in challenging courses at the 4000-level or beyond. Independent study at a high performance level can also contribute to honors. Students interested in any level of honors should consult their major advisors or a member of the Mathematics Major Committee concerning suitable courses. Outstanding performance in the core graduate classes ( MATH 6110   – MATH 6120   , MATH 6310   – MATH 6320   , MATH 6510   - MATH 6520   ) or an excellent senior thesis can contribute to high honors.

Ph.D. students must complete 8 one-semester graduate subjects (96 credit hours), exclusive of thesis, with grades of A or B. At most one of these subjects should be a reading course. Harvard math graduate subjects may occasionally be used, if taken for credit. With prior approval of the Graduate Co-chairs, one relevant advanced undergraduate math subject and relevant graduate subjects from other departments may be used. Note that subjects taken under the graduate P/D/F option cannot be used to fulfill this requirement.

Students are expected to maintain at least a B+ average in each semester. Students in Applied Mathematics must satisfy an additional breadth requirement .

Calculate for all schools

Your chance of acceptance, your chancing factors, extracurriculars, best college majors without significant math requirements.

Math isn't my strongest subject, so I want to avoid majors that heavily rely on it. Can anyone suggest some interesting college majors that don't involve too much math? I'm open to any ideas!

There are plenty of majors that don't involve significant math requirements! Here's a list of majors across different fields that tend to have minimal math components:

1. Humanities: English, history, philosophy, and languages are popular majors that focus on reading, writing, and critical thinking. These subjects typically require little to no math.

2. Social Sciences: Psychology, sociology, political science, and anthropology are great choices if you're interested in understanding human behavior, society, and culture. While some branches of these disciplines do involve quantitative research methods, the core coursework generally doesn't require advanced math skills.

3. Fine Arts: Visual arts, music, theatre, and dance are majors that foster creativity and focus on developing artistic skills. These programs often focus on practical techniques, performances, and portfolio development rather than mathematical concepts.

4. Communication: Public relations, journalism, communication studies, and media studies are all fields centered on effective communication and storytelling. The coursework for these majors revolves around writing, speaking, and creating multimedia content, usually with minimal math requirements.

5. Education: If you're passionate about teaching and working with children, pursuing a major in education might be perfect for you. While math might be required if you specialize in teaching STEM subjects, majors like early childhood education, special education, and English/History education generally don't involve extensive mathematical coursework.

6. Business: While some business majors, like finance and accounting, are known for their heavy emphasis on math, other areas like marketing, human resources, or organizational management often have fewer math requirements.

Keep in mind that each college's curriculum and specific course requirements will vary, so it's essential to explore the degree plan for your desired major at the schools you're interested in attending. Be sure to consider what fields interest you the most, and think about your long-term career goals when choosing a major. Good luck!

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How Burnout Became Normal — and How to Push Back Against It

• Kandi Wiens

Seven strategies to get back to a healthy baseline.

Slowly but steadily, while we’ve been preoccupied with trying to meet demands that outstrip our resources, grappling with unfair treatment, or watching our working hours encroach upon our downtime, burnout has become the new baseline in many work environments. From the 40% of Gen Z workers who believe burnout is an inevitable part of success, to executives who believe high-pressure, “trial-by-fire” assignments are a required rite of passage, to toxic hustle culture that pushes busyness as a badge of honor, too many of us now expect to feel overwhelmed, over-stressed, and eventually burned out at work. When pressures are mounting and your work environment continues to be stressful, it’s all the more important to take proactive steps to return to your personal sweet spot of stress and remain there as long as you can. The author presents several strategies.

If we’re exposed to something repeatedly, it seems we can become desensitized to almost anything. An event that once evoked shock can come to seem routine; what once prompted alarm can eventually inspire no more than a shrug.

• Kandi Wiens , EdD, is a senior fellow at the University of Pennsylvania Graduate School of Education and the author of the book Burnout Immunity : How Emotional Intelligence Can Help You Build Resilience and Heal Your Relationship with Work (HarperCollins, 2024). A nationally known researcher and speaker on burnout, emotional intelligence, and resilience, she developed the Burnout Quiz to help people understand if they’re at risk of burning out.

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