A Math Major's Guide to Choosing Math Courses at UH



Some General Advice

Regardless of your goals or career plans, as you choose courses throughout your math major, you should strive for a mathematics education with the following two qualities:
  1. Breadth: Take a variety of courses that expose you to the ideas from the many diverse branches of mathematics.
  2. Depth: Take courses that help you to become specialized in one or two subdisciplines of mathematics that are related to your future.
These two qualities are competing virtues, so you want to be careful not to obtain one at the cost of the other. To accomplish both, you have to balance your education and make careful choices about the courses you will take. To develop breadth, it is a good idea to take a variety of 3000-level courses to explore different topics in math you think may be interesting. To develop depth, you should take one or two of the 4000-level sequences dedicated to studying an advanced subject in mathematics.

When planning for your future, it is best to begin with the end in mind. Think about what you want to do for a career and think about how you want to use mathematics in that career. Then plan out your courses from now until graduation. You can always alter your plan if your future plans change, but it is better to pick something and head toward it rather than drift aimlessly in the present while you figure out where you are headed.

Do your best to get a clear picture of what you want in your career -- all aspects of it. Then think about what you need to do to accomplish such a career and what knowledge and skills would be useful for you in their pursuit. Select courses and design a degree plan that will help you to learn the things you need and prepare you for what you have to do to obtain your goals. Finally, pursue those goals, and if aspects of your life change (which they inevitably do in at least some capacity) modify your plan to deal with the changes.


Mathematics Degree Programs at UH

At the undergraduate level, the UH Math Department offers B.S. and B.A. degrees in Mathematics. There are two additional options:
  1. Within the B.S. degree there is an Option in Mathematical Finance that can be obtained through additional coursework.
  2. Within each of the B.S. and B.A. degrees, it is possible to also get a High School Teaching Certification by participating in teachHOUSTON and taking additional courses.
Furthermore, there is a B.S. degree in Mathematical Biology that is jointly administered by the Mathematics Department and the Department of Biology & Biochemistry.


Course requirements for all of these programs can be found here:
The NSM Advising website has checklist forms for each degree option that helps you to keep track of the requirements you need:


Math Courses at UH

There is a list of Undergraduate Math Courses on the Math Department Website. However, this list is incomplete and omits many important undergraduate math classes that are regularly offered.

I've created a more complete list here that also includes expanded descriptions of the courses with math majors in mind.

A list of Undergraduate Math Courses at UH with descriptions for Math Majors.




You can also look at the list of graduate courses offered in the UH math department. It is possible for undergraduates to take these courses.


Sequences and Tracks

Sequences

The math department offers certain sequences, which are pairs of courses at the 4000-level that examine an advanced topic in great detail over an entire year. Sequences are split into two courses, a Part I offered in the fall semester, and a Part II offered in the spring Semester.

Here is a list of the sequences the Math Department offers:

Tracks

There are also several pairs of courses that go well together, but are not considered sequences. The following pairs of courses complement each other well. Choose your sequences and tracks carefully. They are your only exposures to advanced topics at the undergraduate level. They not only help you to develop depth in your mathematical education, but the choices you make determine which aspects of advanced mathematics you will gain competency in.


Sample Degree Plans for Math Majors

The following are the course requirements for a B.S. in Mathematics. Note: Although not explicitly stated in the requirements, Calculus I, II, III and Linear Algebra are prerequisites for required courses, and therefore math majors must take these four courses also.

Fitting the Courses into a 4-Year Schedule

To create a schedule that fulfills the course requirements for a math majors, here are some tips to keep in mind.
If you are starting with Calculus I, the following is a fairly typical degree plan.


Sample Degree Plan for Math Majors Beginning with Calculus I
Fall Semester Spring Semester
Year 1 Math 1431: Calculus I
*Other*
*Other*
*Other*
Math 1432: Calculus II
*Other*
*Other*
*Other*
Year 2 Math 2433: Calculus III
Math 2331: Linear Algebra
*Other*
*Other*
Math 3325: Transition to Advanced Mathematics
One of: Math 3334, Math 3335, or Math 3364
*Other*
*Other*
Year 3 Math 3333: Intermediate Analysis
Math 3331: Differential Equations
*Other*
*Other*
Math 3330: Abstract Algebra
Math Elective
*Other*
*Other*
Year 4 4000-level Sequence, Part I
Math Elective
*Other*
*Other*
4000-level Sequence, Part II
Math 4389: Survey of Undergraduate Mathematics
*Other*
*Other*

Note: The courses listed *Other* can be from other departments or other math courses. In particular, *Other* courses can be used to fill general degree requirements or be used for a minor or second major from another department.

Note: One Math Elective must be a 4000-level math course.

Note: Math 3333 and Math 3330 can be completed in either order or taken concurrently.



If you are starting with Precalculus, then you can modify the above schedule to delay calculus courses by one semester. To stay on track, it is a good idea to take three Math courses some semester; possibly in the fall semester of year three.


Sample Degree Plan for Math Majors Beginning with Precalculus
Fall Semester Spring Semester
Year 1 Math 1330: Precalculus
*Other*
*Other*
*Other*
Math 1431: Calculus I
*Other*
*Other*
*Other*
Year 2 Math 1432: Calculus II
Math 2331: Linear Algebra
*Other*
*Other*
Math 3325: Transition to Advanced Mathematics
Math 2433: Calculus III
*Other*
*Other*
Year 3 Math 3333: Intermediate Analysis
One of: Math 3334, Math 3335, or Math 3364
*Other*
*Other*
Math 3330: Abstract Algebra
Math 3331: Differential Equations
*Other*
*Other*
Year 4 4000-level Sequence, Part I
4000-level Math Course
*Other*
*Other*
4000-level Sequence, Part II
Math 4389: Survey of Undergraduate Mathematics
*Other*
*Other*

Note: The courses listed *Other* can be from other departments or other math courses. In particular, *Other* courses can be used to fill general degree requirements or be used for a minor or second major from another department.

Note: Math 3333 and Math 3330 can be completed in either order or taken concurrently.



If you are starting with Calculus II, you have a lot more freedom and there are many possible ways to arrange your schedule. Also, if you can Linear Algebra in spring of your first year, you can make room for more math classes in later years. Here is one possible degree plan in this situation.


Sample Degree Plan for Math Majors Beginning with Calculus II
Fall Semester Spring Semester
Year 1 Math 1432: Calculus II
*Other*
*Other*
*Other*
Math 2433: Calculus III
Math 2331: Linear Algebra
*Other*
*Other*
Year 2 Math 3325: Transition to Advanced Mathematics
One of: Math 3334, Math 3335, or Math 3364
*Other*
*Other*
Math 3333: Intermediate Analysis
Math 3331: Differential Equations
*Other*
*Other*
Year 3 Math 3330: Abstract Algebra
Math Elective
*Other*
*Other*
Math Elective
Math Elective
*Other*
*Other*
Year 4 4000-level Sequence, Part I
Math Elective
*Other*
*Other*
4000-level Sequence, Part II
Math 4389: Survey of Undergraduate Mathematics
*Other*
*Other*

Note: The courses listed *Other* can be from other departments or other math courses. In particular, *Other* courses can be used to fill general degree requirements or be used for a minor or second major from another department.

Note: One Math Elective must be a 4000-level math course.

Note: Math 3333 and Math 3330 can be completed in either order or taken concurrently.

More Specific Degree Plans Based on Your Aspirations for the Future

Here are some more specific Sample Degree Plans based on your future aspirations (e.g., specific kinds of jobs or graduate school). Some also describe how to schedule for the "Option in Mathematical Finance" or to obtain Teaching Certification.

Miscellaneous Pieces of Advice








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