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 you take?
• What do we learn in these courses?

What courses should you take?

1. First year students:

   1. If you have not received high school credit for precalculus or need a refresher, take Precalculus (Math 112).
   2. If you have not received college credit for calculus, take Calculus 1 (Math 221).
   3. If you are taking Calculus 1 now, take Calculus 2 next (Math 222).
   4. If you are taking Calculus 2 now, take Calculus 3 next (Math 223). If you want to take more than one math class, consider Math 233 as well.
   5. If you are in Calculus 3 now, you should next take Math 233 or Math 326 (or both). If you want to take more than one math class and you already completed Math 233, consider Math 239 as well.

2. Second year students:

   1. If you haven't yet, finish the calculus sequence.
   2. Finish which ever you haven't taken yet: Math 233 or Math 239
   3. Consider Math 326 and Math 360.

3. Third and fourth year students:

   1. If you haven't finished Calculus 3, Math 233, or Math 239, do it now!!
   2. This is where you have a little more freedom in choosing courses. Make sure you know the requirements for the math degree you are seeking and then choose your courses according to your needs/interests:
      • Secondary Certification: In addition to Math 324 (Real Analysis), your program requires you to take Math 335 (Foundations of Geometry), Math 330 (Abstract Algebra) and Math 360 (Probability and Statistics). For your electives, some particularly good choices are Math 390 (History of Math), Math 319 (Number Theory) and Math 326 (Differential Equations). But choose according to your interests and choose as many as possible. Your excitement about mathematics is the key to being a great teacher!
      • Graduate Studies in Math: Take all the math you can!! Really! Math 330 (Abstract Algebra) is a must. You should take both Math 330 and Math 324 (Real Analysis) before the end of your junior year. (Questions about both courses show up on the GRE's.) When you have completed 324, consider 325 (Real Analysis II). Math 370 (Complex Analysis) is also a good choice. If your interest is more on the analysis side or the applied side, take any or all of our Differential Equations courses (326, 328, and 372) and Numerical Analysis courses (345 and 346). If you are more inclined to algebra, take Math 333 (Linear Algebra II) or Math 319 (Number Theory). Topology will probably be required in graduate school, so you may want to get an early start with Math 338 (General Topology). Combinatorics (Math 315) offers many research opportunities. Be looking for our special Math 380 offerings as well.
      • Statistician or Actuarial Studies: Take Math 360 and 361 (Probability and Stats I and II). If you have taken Math 345 (Numerical Analysis I), then 346 (Numerical Analysis II) is a good choice. Math 326 (Differential Equations) and 372 (Partial Differential Equations) are also good choices. If you are interested in the actuarial field, investigate a Business minor. Take financial accounting, micro economics, and macro economics. Learn EXCEL really well. If you are interested in Stats but not actuarial work, look for a minor in another discipline to which you can apply the stats: biology, economics, psychology, etc.
      • Career in Applied Math: Math 326 (Differential Equations) and Math 319 (Number Theory) and Math 360 and 361 (Probability and Stats I and II) are important. Numerical Analysis (Math 345 and 346) for highly recommended as well for all applied mathematicians. The Linear Programming and Operations Research Course (Math 332) is recommended for those inclined towards financial math, business or economics. On the discrete side of applied math, both Math 315 (Combinatorics) and statistics are particularly valuable. Math 333 (Linear Algebra II) is also a very good idea for applied mathematics. You should consider taking additional computer science and/or physics. Try to learn Maple or Matlab and also Java or C++.

What do we learn in these courses?

1. Basic Courses
2. Advanced Courses

1. Basic Courses

   • 112 Precalculus. This course is meant to be a preparation for calculus. You will learn and/or enhance your algebra skills, and you will also cover trigonometry.

     Who is 112 for? This course is designed primarily for the student who needs a foundation in algebra and trigonometry for the study of Calculus.

   
   
   • 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. Computer scientists may want to take it because it is a prerequisite for other courses that they may want to elect.

   
   
   • 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!

     Who is 222 for? Still everyone! Majors, minors, concentrators, dabblers, and science majors. Computer scientists may want to take it because it is a prerequisite for other courses that they may want to elect.

   
   
   • 228 Calculus II for Biologists. You will study somewhat different topics than in Math 222, with everything geared more towards biologists! Also like 222, it is best to take this immediately after Calculus 1. NOTE: If you plan to take Calculus 3 or Differential Equations, you should take Math 222 instead. This course is basically for bio majors who don't plan to take any math beyond Calculus 2.

     Who is 228 for? Bio majors!!! Minors are also welcome to take 228. This is not for math 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). It's good to take immediately after Calculus 2.

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

   
   
   • 233 Linear Algebra I. This course studies straight/flat things like lines and planes. It deals with how to use matrices as functions. You will find out all about vectors. You should take this is your sophomore year, at the latest. Right after Calculus 2 is good.

     Who is 233 for? It is for majors, concentrators and minors. Computer scientists may want to elect it because it is crucial for computer graphics and animation. It is also very useful for physicists and other scientists because there are so many applications of it.

   
   
   • 237 Introduction to Discrete Mathematics. This is about logic and set theory and combinatorics and graph theory and lots of fun stuff that does not involve calculus. This course is NOT for math majors or math concentration students.

     Who is 237 for? It is not available for the math major or for education students with a concentration in math, but it is an option for minors and computer scientists.

   
   
   • 239 Introduction to Mathematical Proof. This does exactly what the title says. You will get the skills necessary to write rigorous mathematics, just like the books! You will learn how to read math too.

     Who is 239 for? All math majors. Minors, computer scientists, and concentrators have the options of taking 239. You should take this in your sophomore year or, at the latest, the first semester of your junior year.

   
   

2. 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-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! Learn to chuckle when someone tells you that a googleplex is a big number!

     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 if we can't understand sets, how can we hope to understand the Riemann Hypothesis?

   
   
   • 319 Theory of Numbers. Prime time for prime numbers! Number theory is about the primes?sounds easy, but facts about primes are tricky to come by. Learn how and learn about encryption schemes along the way.

     Who should take 319 and when? This course can be taken any time after 239. 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. All the stuff we whooshed over in Calculus 1 is done rigorously. It is absolutely crucial for teachers who might teach AP calc and for anyone planning on doing any advanced math or statistics.

     Who should take 324 and when? Everyone majoring in math must take 324. 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 1 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. Note: It is offered every other spring semester.

   
   
   • 326 Differential Equations. This course is the natural continuation of Calculus. Solving a differential equation is really integration in disguise. There are great applications to biology and physics and to everyday life.

     Who should take 326 and when? Anyone interested in mathematical modeling or engineering. 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 may be a good idea to take Math 233 before this or concurrently.

   
   
   • 330 Abstract Algebra. This course studies addition and multiplication and "solving for x" in a very strange way: It investigates groups (just multiplication) and rings (multiplication and addition). That doesn't help much but it is very interesting! It further generalizes some of the notions from Linear Algebra (Math 333).

     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, the Assignment Problem, Dynamic Programming, Integer Programming, and Game Theory.

     Who should take 332 and when? Anyone who has had linear algebra (Math 233) and a programming course, not because this is a "coding" course, but because you will need to follow and implement algorithms into some "canned" programs. Also, anyone who is interested in financial math, business, or economics, or anyone interested in "real-world applications".

   
   
   • 333 Linear Algebra II. This is a more theoretical version of Math 233. Depending on the professor, there may or may not be a lot of applications taught in this course. Either way, it provides a good foundation for graduate school. 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, just to name a few.

     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 a continuation of Math 233, so it might be good to take it as soon as you can after Math 233 and Math 239.

   
   
   • 335 Foundations of Geometry. This course looks at familiar geometric concepts like similarity and congruence in many different contexts. It also looks at the relation of geometry to its axiomatic underpinnings.

     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 General Topology Simply put, this course is all about open sets. Topology is the study of spaces and sets and can be thought of as an extension of geometry. Take this course if you want to find out why a square and a circle are really the same thing. Did you know that a donut and a coffee mug are the same?

     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 application 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? An elective course, it is great for people looking for interdisciplinary applications of mathematics. People interested in research work in biomath should definitely take the course as soon as possible.

   
   
   • 345 Numerical Analysis. The course is a combination of theory, applications, and computations. The course revolves around finding 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 determine the accuracy of the solutions, especially if the actual solution is not known.

     Who should take 345 and when? This course is especially important to math and science majors, and it forms the basis for many areas of applied mathematics and actuarial science. You should consider taking it soon after completing Math 233 and Math 239.

   
   
   • 348 Oral Presentation and Research Seminar. This is a one-credit elective. 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, who is not in the certification program. Really, anyone who wants an experience getting up-close and personal with math that doesn't come from a textbook and who would like to develop presentation skills.

   
   
   • 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 and Statistics I. No mystery here.

     Who should take 360? Just about everyone. It is required of majors seeking secondary certification. It can replace 262 for the math minor or math 242 or 262 for the math concentrator. It is a critical course for those interested in actuarial science, a career in finance or business, or a career in any applied math field.

   
   
   • 361 Probability and Statistics II. A continuation of guess what.

     Who should take 361? Like 360, it is a critical course for those interested in actuarial science, a career in finance or business, or a career in any applied math field.

   
   
   • 366 Mathematical Foundations of Actuarial Science. This course does not count towards the major.

     Who should take 366? Well, duh, anyone looking to take the actuarial exams. But it will also provide some review for the subject test of the Math GRE.

   
   
   • 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 inter-disciplinary 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 of choice. The loop is closed with students presenting a group project at the end of the semester dealing with a real-world application of wavelets.

     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. Make sure you have linear algebra and proof and a computing course before you do!
     
     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!

   
   
   • 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.

   
   

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