Advisement Material for Math Concentration

Advisement Material

The purpose of this page is to give you, the student, some extra information about the various courses we offer in the Department of Mathematics. It is currently a "work in progress" and should not be considered as a complete, comprehensive description of all available courses. It should also not be considered as a replacement to your academic advisor. We simply provide this information to you as additional assistance as you plan your undergraduate career.

Below you will find useful information about math courses that are particularly good for different career paths, and you will find a bit more information about particular courses. For more information about a particular course see the Course Catalog and Course Rotation pages.

For specific degree requirements, see the Program Descriptions.

What courses should I take as an Elementary Education Major with Concentration in Mathematics?

In addition to the required courses for all Elementary Educations majors of Math 140 and Math 141:

  1. If you have not received high school credit for precalculus or need a refresher, take Precalculus (Math 112). Note that this does not count towards the Concentration.

  2. If you have not received college credit for calculus, take Calculus 1 (Math 221).

  3. If you have completed Calculus 1, take Calculus 2 (Math 222) next.

  4. If you have completed Calculus 2, take either Calculus 3 (Math 223) (* see 5 below) or Linear Algebra I (Math 233).

  5. You will need a statistics course: Select one from Math 242, Math 262, Math 341, Math 361. If you choose to take Probability and Statistics (Math 341), you will need Calculus 3 as a pre-requisite. If you choose to take Statistics (Math 361) - offered Spring only - you will need Calculus 3 and Probability (Math 360) as pre-requisites.

  6. If you have not yet taken Introduction to Proofs (Math 239), take it as soon as possible. Do NOT take Discrete Mathematics (Math 237).

  7. Take Geometry (Math 335), which is offered only in the Spring semester. Introduction to Proofs is the pre-requisite for this course, not Discrete Math.

  8. Take Advanced Mathematics Topics for Early Childhood and Childhood Education (Intd 376).

Note: Math 242, and Math 262 will not count towards the Math major.

Note: All courses must be completed with a grade of C- or better in order to count towards the Concentration.

What do we learn in these courses?

Basic Courses

Advanced Courses

Basic Courses

  • 221 Calculus I. This is a course that tells a wonderful story and gives you practical skills to boot. The story is about three questions: What is instantaneous rate of change? What is the area under a curve? How are they related? While the story was first told more than 300 years ago by Newton (or was it Leibnitz?), the answers to the questions posed continue to underpin much of what we do in practical and theoretical math today.

    Who is 221 for? Everyone! Majors, minors, concentrators, dabblers, and science majors.

  • 222 Calculus II. Got more calc? Yes! You will study more about integration and learn about the logarithm and exponential functions. You will learn about sequences, series, and lots of other things too. It is best to take this immediately after Calculus 1. You don't want to forget anything – it the second chapter in the saga.

    Who is 222 for? Still everyone! Majors, minors, concentrators, dabblers, and science majors.

  • 223 Calculus III. This course is like Calculus 1 but instead of curves in the two dimensional plane, we study curves and surfaces in 3 dimensional space. You will learn about derivatives (partial derivatives) and about integrals (This time, we will compute volumes instead of areas because the dimension went up).

    Who is 223 for? All majors and minors. Concentrators can take it, but they don't have to. It develops a sense of spatial mathematics useful for computer graphics and all visualizations.

  • 230 Programming and Mathematical Problem-Solving. Mathematics is deeply linked with computer programming, and in this course you will learn how. You will learn to use a programming language to express calculations taken from many important mathematical problems, but more importantly you will learn how programming can help you understand mathematical ideas by putting them into a tangible form.

    Who is 230 for? All mathematics majors and ONLY math majors. Take this course along with Calculus 2, or as soon as possible thereafter.

  • 233 Linear Algebra I. This course studies system of linear equations arising in many areas of mathematics, and real-world applications. This course also serves as a bridge to higher mathematics. You will learn about vector spaces, linear independence, and spanning. You should take this early in your sophomore year, at the latest.

    Who is 233 for? It is for majors, concentrators, and minors. It is also very useful for business, economics, statistics, physicists and other scientists because there are so many applications of it.

  • 239 Introduction to Mathematical Proof. This does exactly what the title says. You will get the skills necessary to write rigorous mathematics.

    Who is 239 for? All math majors and math concentrators. Minors have the option to take this. You should take this in your sophomore year, at the latest.

Advanced Courses

  • 301 Mathematical Logic. What is a mathematical object? What is a mathematical proof? What does it mean to prove something? This course will make you investigate your assumptions about how mathematics is done and what the limits of mathematics are.

    Who should take 301 and when? Definitely after you've taken 239 and are comfortable with abstract arguments. A course that is good for those going on to graduate work in mathematics, philosophy, or computer science. Also good for those who just enjoy thinking about the fundamentals of our subject.

  • 302 Set Theory. Sets are the basis of everything in mathematics! Learn what we assume about sets and what we can prove about them. Spend time getting acquainted with infinite ordinals and infinite cardinals!

    Who should take 302 and when? This is an abstract course, so you should be comfortable with writing proofs and thinking hard about unusual things. So take it after 239 and perhaps not as your first 300-level math course. A great course for students planning on graduate school, and for those who want to really investigate sets and some crazy large numbers.

  • 303 Theory of Computational Complexity. When is a calculation that takes all night to finish "fast"? When the alternative needs more than the remaining lifetime of the universe to finish. Take this course to find out why we believe there are such calculations, and to explore a frontier of math and computer science still fraught with important but unanswered questions.

    Who should take 303 and when? Take this course if you are interested in the connections between mathematics and computer science. This course is about the logical analysis of algorithms rather than their programming, so take it after 239. Other than that prerequisite, take it as soon as you can if you want it, since it's not offered all that often.

  • 304 Theory of Computability. What does it mean to compute? A seemingly simple question that didn't get answered until the 1930s, and then with the immediate consequence that despite the very real successes of computing, most things actually aren't computable at all. Find out where all of this comes from and what it means, and make some neat connections to mathematical logic in the process.

    Who should take 304 and when? This is another good course for students interested in the shared foundations of mathematics and computer science. It's also fun for students who like proofs and logic—such students might consider it part of a package along with Math 301 and/or 302 to spread through their third and fourth years. Be ready for lots of proofs, particularly ones involving constructions, contradiction, and the occasional induction; this is definitely something to take after Math 239.

  • 315 Combinatorics. Combinatorics is counting. Counting is not as easy as it sounds, but it is as universally useful as it appears. We explore a wide variety of the "how many ways" questions. We start with familiar, and build beyond, but always keeping connected with easily understood questions.

    Who should take 315 and when? This is an excellent first course after proofs (or even 237). It is relevant to all of mathematics - everywhere counting appears. It shows up in many applied contexts, and in many theoretical situations. Furthermore, the simple questions with sophisticated answers make great examples for secondary students.

  • 319 Theory of Numbers. Prime time for prime numbers! Number theory is about truly understanding how numbers work, with an emphasis on primes. This may sound simple, but facts about primes are not easy to come by. Learn why primes make modular arithmetic function well. Along the way we will see how we can use their complicated structure to form nice encryption schemes.

    Who should take 319 and when? This course can be taken any time after 239, though 233 is recommended too. It gives valuable insight into the nature of the natural numbers that is valuable to future teachers. It can introduce potential researchers to a rich and active field. It can also open career opportunities.

  • 324 Real Analysis I. This takes the Proofs course (239) and applies it to aspects of Calculus 1. The theory behind Calculus is proven rigorously. It is absolutely crucial for all math majors, especially for teachers who might teach AP calc, and for anyone planning on doing any advanced math or probability.

    Who should take 324 and when? Everyone majoring in math must take this course. Anyone who is trying to expand a minor or a concentration so as to leave open the possibility of future study in math should take it. When to take it? After Math 239. If you are planning to do advanced work in mathematics (graduate school, perhaps) you should take this course as early as possible. The first semester of the junior year is best. However, if you were not totally comfortable with Math 239, you should wait a bit, and take one or two other 300-level electives before taking Math 324.

  • 325 Real Analysis II. This continues Real Analysis I by going deeper into concepts you already know, and by introducing new contexts for analysis, line Rn, metric spaces, and spaces of functions. It's all about convergence.

    Who should take 325 and when? This course is a must for any one who intends to enter a PH.D. program in mathematics or statistics or any mathematical science.

  • 326 Differential Equations. This course is the natural continuation of Calculus. If you want a good reason to take Calculus, this course is it. Differential equations are equations that involve functions and their derivatives. There are great applications to finance, economics, biology, physics and, really, to everyday life.

    Who should take 326 and when? Anyone interested in mathematical modeling or engineering. This course is required for the BS in Applied Mathematics. It is required of physics majors, and very useful to any scientists. If you really liked calculus, this is the course for you. If you want to do financial engineering or economics, this course is for you. When? As soon as possible after Calc 3. It is a good idea to take Math 233 before this.

  • 328 Theory of Ordinary Differential Equations. This course is a continuation of Math 326 covering existence theory in a metric for the scalar differential equation via Picard iterations and the Fixed Point Theorems. Phase plane analysis of two dimensional linear and nonlinear systems, including bifurcation theory, stability and limit cycles, index theory, and the Poincararé-Bendixson Theorem. A variety of applications to population, and ecological models and physical systems will be covered.

    Who should take 328 and when? Students who enjoyed differential equations who want to see the theoretical side of DEs, systems of DEs, applications. Take it whenever it is offered after Math 326. It’s only offered every other fall of odd years!

  • 330 Abstract Algebra. The basic premise of abstract algebra is to extract the basic properties of algebra as you know it from high school algebra and linear algebra and abstract them to be used in more general ways. In previous algebra classes we tend to study a certain set of objects, such as numbers or functions or matrices, and learn about their algebraic properties. In abstract algebra, we begin with the basic properties and structure, without much emphasis on the objects they are applied to. This means we will study algebraic properties apart from concrete realities, specific objects, or actual instances. Many of the topics we will learn in this abstract algebra course can be applied within other areas of mathematics and other scientific realms, including physics, chemistry, coding theory, neuroscience, and many others.

    Who should take 330 and when? Almost everyone! It is required for anyone in the secondary certification program. It is absolutely necessary for anyone contemplating graduate school. It is a good elective for concentrators and computer scientists. Students bound for graduate school may want to take it before the end of their junior year. However, if you were not totally comfortable with Math 239, you should wait a bit, and take one or two other 300-level electives before taking Math 330. It is not necessary to take Math 333 first, but it may be beneficial to do so.

  • 332 Linear Programming and Operations Research. This is a course that picks up where Elementary Linear Algebra leaves off with linear systems, extends it to systems of linear inequalities, and does some really cool real-world applications, mostly dealing with optimization. If you're looking for a course with plenty of math applications, this is it! Students will learn what operations research problems are, how to formulate them, and to master different techniques for solving them. Topics to be covered may include the Simplex Method, Duality, Network Optimization Models (including Maximal Flow and Minimal Spanning Trees), Dynamic Programming, Integer Programming, and Game Theory. Students work on a group project for at least two weeks at the end of the semester with a real-world application. Students will write up and submit their models or results prior to presenting the project to the class and invited faculty. Recent projects include: Evacuation Planning, Cancer Therapy, Optimal House Design, Waste Collection, Solving Sudoku, and more!

    Who should take 332 and when? Anyone who has had Linear Algebra (Math 233), Intro to Proofs (Math 239) and a programming course (Math 230), not because this is a "coding" course, but because you will need to follow and implement algorithms. Anyone who is interested in financial math, business, data science, economics, or "real-world applications" should take this course.

  • 333 Linear Algebra II. This is a more theoretical version of Math 233. Depending on the professor, there may be applications taught in this course. Either way, it provides a good foundation for graduate school. This course is required for the BS in Applied Mathematics. You will dive much deeper into vector spaces but in a more abstract setting. More on linear transformations, matrices, eigenvalues, and eigenvectors from both an algebraic and geometric perspective. Linear algebra is especially helpful in many areas of applied math, e.g. in solving linear systems of ODEs, in finding numerical solutions of PDEs, in setting up and solving linear programming problems, in applied matrix theory, in high-level statistics, and in quantum mechanics.

    Who should take 333 and when? Most math majors should probably take this one, but especially anyone planning on going to graduate school should take it. It is required for the BS in Applied Mathematics. It is a good course for Actuarial students. It is good for anyone considering an advanced degree in statistics or data science. As it is a continuation of Math 233, it is a good idea to take it as soon as possible after Math 233 and Math 239.

  • 335 Foundations of Geometry. In this course you learn that geometry is plural. There are several different geometries, each having a different relation to how we think and see the world around us. It includes the very basics, and demonstrates that sometimes by asking very simple questions, one can find very sophisticated answers.

    Who should take 335? It is required of all concentrators and of all majors looking for secondary certification. It is a good elective for any math student.

  • 338 Topology. How does mathematics look without distance, without angles, without measurements? That is topology. It is about open sets, surfaces, and knots. Topology is the study of spaces and sets and can be thought of as an extension of geometry. It is a completely different way to experience the world around you, and the mathematics beyond.

    Who should take 338? This course requires a certain level of mathematical sophistication and a lot of imagination. If you are planning on going to graduate school, you should probably take this course. It would also be a good course for anyone who enjoys abstract thought that may surprise you or even blow your mind (in a good way)!

  • 340 Modeling Biological Systems (Lecture and Lab). The course looks at applications of mathematical modeling techniques in Biology. Cross-listed as Bio 340, it is usually a nice mix of people from the two majors, with different strengths and different challenges. The lab is computer-based.

    Who should take 340? As an elective course, it is great for people looking for interdisciplinary applications of mathematics. People interested in research work in biomathematics should definitely take the course as soon as possible.

  • 341 Probability and Applied Statistics. The goal of this course is to give students a one-semester introduction to the field of probability theory, which includes basic counting techniques, random variables and their probability distributions, multivariate distributions, and theoretical means and variances of these variables. In addition, this course will introduce you to the field of applied statistics and you will learn how to use data to make informed decisions.

    Who should take 341? Anyone who wants to learn about both probability and statistics but does not plan on pursuing a career related to statistics.

  • 345 Numerical Analysis I. The course is a combination of theory, applications, and computations relating to numerical approximations of solutions. The course revolves around deriving algorithms (or recipes) from theorems, mostly from calculus or linear algebra, to find approximations of solutions to problems where exact or analytical solutions are too difficult or impossible to find. Another important aspect of the course is learning how to analyze the accuracy of the solutions, improve the accuracy, and improve convergence rates.

    Who should take 345 and when? This course is required for the BS in Applied Mathematics. It is especially important to math and science majors, and it forms the basis for many areas of applied mathematics and actuarial science. The course requires coding. You should consider taking it soon after completing Math 230, Math 233, and Math 239.

  • 346 Numerical Analysis II. With a firm foundation from Numerical 1, more interesting topics such as Least Squares, Fast Fourier Transforms, finding eigenvalues and eigenvectors numerically, solutions to ODEs and systems of ODEs, and other topics may be covered.

    Who should take 346 and when? Preferably the semester after 345 (it is only offered every other spring). Students interested in numerical analysis as a field, or those who want a BS in Applied Mathematics.

  • 348 Oral Presentation and Research Seminar. This is a one-credit requirement. Students will learn presentation techniques, and library techniques. Everyone in it will read an appropriate journal article and make a presentation.

    Who should take 348? Officially, anyone needing to satisfy the oral-research presentation requirement in math, who is not in the certification program. This requirement may be waived through other approved math courses, or approved presentations. The requirement is satisfied by INTD 302 for students seeking secondary certification.

  • 350 Vector Analysis. This course is really a follow up to Calc 3. It will look again at calculus in higher dimensions and extend your notions of integration and differentiation.

    Who should take 350? Anyone who liked Calculus 3 and who likes thinking about those hard to imagine objects that occur in dimensions higher than 3. This course is great for anyone who does physics.

  • 360 Probability. Calculus-based probability course.

    Who should take 360? The goal of this course is to give students a one-semester introduction to the field of probability theory, which includes basic counting techniques, random variables and their probability distributions, multivariate distributions, and theoretical means and variances of these variables. It is a critical course for those interested in actuarial science, a career in finance or business, or some careers in an applied math field. It is an option for majors seeking secondary certification (provided that you also take Math 361). It can replace 262 for the math minor or math 242 or 262 for the math concentrator if taken with 361. Essential for anyone wishing to specialize in statistics.

  • 361 Statistics. Probability based statistics course.

    Who should take 361? The goal of this course is to give students a one semester probability based statistics course. Like 360 (Probability), it is a critical course for those interested in actuarial science, statistics, data analysis, a career in finance or business, or some careers in an applied mathematics field. With 360, it counts as the Probability and Statistics requirement for Secondary Education students. This course is essential for anyone wishing to specialize in statistics.

  • 363 Regression and Time Series. Covers multilinear regression and time series models. This course is particularly for those interested in actuarial studies. It should be taken after 361 (statistics).

    Who should take 363? Students interested in a career in actuarial science or statistics. Permission of instructor is required.

  • 366 Mathematical Foundations of Actuarial Science. This course prepares you for the first actuarial exam (Exam P – Probability).

    Who should take 366? Anyone interested in the actuarial career and taking the actuarial exams. It will also provide some review for the subject test of the Math GRE. Permission of instructor is required.

  • 371 Complex Analysis. Complex analysis begins as being approximately equivalent to Calculus II, but with complex numbers, and leads to some amazing applications. However, it takes some time getting there, and there is so much more. Along the way it passes through complex arithmetic, algebra, trigonometry, and geometry. The culmination explores properties of limits, derivatives, series, and integrals with complex numbers. Overall it allows for a unifying view of many properties of real-valued calculus that can be seen more clearly when recognizing that they sit within the larger framework of the complex numbers.

    Who should take 371? Complex analysis has connections to most other branches of mathematics. It is especially useful for many applied areas of mathematics, including ordinary and partial differential equations, dynamical systems, and wavelets, as well as, applications in physics and electrical engineering, due to the ability to represent complete solutions, both periodic and transient. Here is just a sample: problems involving vibrating strings and membranes, Laplace’s equation, the heat equation, the wave equation, and signal processing. It also makes for a good experience to tie together a vast amount of secondary school mathematics with the concepts of calculus.

  • 372 Partial Differential Equations. Di?erential equations that involve two or more independent variables are called partial di?erential equations. They play a central role in many problems in applied mathematics and in the physical and engineering sciences. Topics include first-order equations, the most essential second-order linear equations, and some methods for solving such equations, including numerical techniques. Modeling for the motion of a vibrating string, (wave equation), and conduction of heat in a solid body, (diffusion equation, Laplace’s equation) are emphasized.

    Who should take 372? Students who enjoyed ordinary differential equations and/or would like to apply mathematics to sciences. Take it whenever it is offered after Math 326. It’s only offered spring of even years!

  • 376 Financial Mathematics. This course prepares you for the second actuarial exam (Exam FM – Financial Mathematics).

    Who should take 376? Anyone interested in the actuarial career and taking the actuarial exams. Permission of instructor is required.

  • 380 Topics in Math. This is a "special topics" course, and the details vary from offering to offering, depending on the instructor. If there is a particular topic you'd like to learn about that is not covered in great detail in another course, see if you can find a professor to teach it as a Topics in Math course.

    Click here for a list of some past Topics courses.

    Who should take 380? This elective is perfect for students who are looking for a three hour course and who are interested in the particular topic being offered that semester. Certainly consulting with the faculty member in charge of the course would be a good ides.

  • 382 Introduction to Wavelets and Their Applications. This is an interdisciplinary course that bridges the gap between theoretical, applied, and computational math using a "hands-on" approach. The course begins with manipulating digital audio and images with linear algebra to drive the theory, and quickly moves into areas of complex analysis and Fourier series to develop Haar and Daubechies wavelet transforms. Matlab is used as the computing language. Students work on a group project for at least two weeks at the end of the semester with a real-world application of wavelets. Students will write up and submit the results and code prior to presenting the project to the class and invited faculty. Recent projects include: Breaking Captchas, Predicting Oil Futures, Compression of Sound and Image Files, Detecting Handwriting and Art Forgeries, Image Identification, FBI Fingerprint compression, and more!

    Who should take 382? This elective is perfect for students who want to see how theory and application work in tandem to produce some real-world results. The course requires coding. Students should take 233, 239, and 230 prior to taking this course.

  • 383 Biomathematics Seminar. A seminar course where current research papers in biomathematics are read and discussed by the class. One hour credit.

    Who should take 383? People interested in the current state of research in mathematical biology. Almost required for people doing research projects in the area, but guaranteed to be interesting to anyone who is both a mathematics major and a biological organism.

  • 384 Computational Graphics. Computer graphics, the thing that makes modern video games and movies work. And almost all of it boils down to the highly optimized integration of certain functions over space and sometimes a few other dimensions. Open the hood on a technology that most people enjoy every day, and behold teeming masses of calculus and linear algebra inside.

    Who should take 384 and when? Take this course if you are interested in the computational aspects of applied math, or just want to know how computer graphics works. You will do some programming in this course, so take it after 230, and maybe after another course or experience that builds your programming skills. You also need to be comfortable with material from Math 223 and parts of 233.

  • 390 History of Mathematics. An overview of who, what, where, when, and why for all of mathematics up to your undergraduate courses.

    Who should take 390? Anyone who wants to know the story of mathematics and not just the details.

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