Math Major Advising

As of Fall 2012, I am a math major adviser. If you are interested in majoring in mathematics, feel free to contact me.

Advising FAQ

When should I start planning a math major?
Immediately! It is never too early to get started. University guidelines do not require you to declare a major until after your sophomore year, and Department guidelines require you to have taken an upper-division class or a freshman seminar before declaring. Neither of those requirements means you can't set up an appointment to help plan your major as a freshman.

How should I plan for a math major?
Take a look at the math major requirements. You'll need: three calculus courses and a freshman seminar; the algebra and analysis sequences; complex analysis and PDE; and electives. Most math elective courses have particular prerequisites--think about not only which courses you'll take, but also what order you'll take them in! I've provided some sample major plans to the right.

What can I expect as a math major?
In the lower division classes (e.g. the calculus sequence MATH 104, 114, 240, 241), coursework emphasizes computational skill and practice, as well as introduction to some basic mathematical objects. Familiarity with computation and these basic objects is the base upon which much of the upper-division coursework builds.

In some upper-division classes, you'll learn to abstract the essential features of the objects you learned about in the calculus sequence. Topics addressed in these courses include fundamental questions like What is a number?, What is a function?, and What is multiplication?. In these courses, students investigate reasons behind the theorems of the calculus sequence, as well as generalizing those theorems to broader contexts.

Other upper-division courses will introduce branches of mathematics you may not have previously encountered, such as combinatorics, number theory, differential geometry, topology, and game theory.

Generally, for major courses, you can expect to spend at least 15 hours outside of class on homework and required reading. Of course this is only an estimate. Depending on the particular course, instructor, and student, you may need to spend more or less time outside of class.

What is Honors Calculus?
The Honors Calculus sequence (MATH 116-260) is a two-semester course which covers multivariable calculus, differential equations, and some linear algebra. It is a more theoretical approach to the material than the 114-240 sequence. For this reason I strongly advise students who are planning to major in mathematics to take 116-260 instead of 114-240.

What are Freshman Seminars?
As a mathematics major, you'll learn how to read and write proofs. While it is possible to pick up this skill on-the-fly, the Freshman Seminars (MATH 202 and 203) are designed to introduce students to the concept of proof, how to read proofs, and several basic proof techniques. These skills are absolutely essential to upper-division courses. Like any skill, proofwriting grows with practice over time, so getting started early is helpful, and that's what the Freshman Seminars are for.

Students who have taken the Honors Calculus sequence may not need a Freshman Seminar; consult a math major adviser or the professor teaching the Freshman Seminar to determine what the right choice for you is.

What about waivers and advanced placement?
It's general policy to allow students to waive a class if they have successfully completed a ``later" class. For example, successful completion of MATH 114 waives the requirement to take MATH 104. You can also place out of calculus courses by taking a written exam of comparable content to the final exam for that course.

What is the difference between 300 level courses and 500 level courses?
The topics covered in, for example, MATH 360 and MATH 508 are largely the same. 500 level courses are taught with a more theoretical approach and may go into somewhat more depth on certain topics. Both 360/361 and 370/371 satisfy the same requirements as their 500-level counterparts. The 500 level courses generally will require significantly more time and effort.

I'm not sure which level of class to take.
Try sitting in both a 300-level class and its 500-level counterpart for the first week or two. Just make sure you keep up with the first few assignments for both classes, so that whichever one you pick, you won't be behind.

Math Major Requirements

• Calculus: MATH 104; MATH 114 or MATH 116; MATH 240 or MATH 260
• Freshman Seminar: MATH 202 or MATH 203
• Algebra: MATH 370 or MATH 502; MATH 371 or MATH 503
• Analysis: MATH 360 or MATH 508; MATH 361 or MATH 509
• Complex analysis: MATH 410
• Partial differential equations: MATH 241 or MATH 425
• Mathematics electives: MATH courses numbered at least 300, for a total of 13 c.u.

MATH 241, MATH 410, MATH 425

As of Fall 2012, the syllabus for MATH 241 has changed. As a result, MATH 241 now satisfies the PDE requirement, but not the complex analysis requirement. This means students declaring a math major Fall 2012 or later must take MATH 410, which is generally offered only in the Fall Semester.

Useful experiences to have

Apart from the requirements for the major, you should consider the following:

• Take a linear algebra course. MATH 312/512 and 313/513 are courses in linear algebra. While they are not required for the major, the topic is invaluable in mathematics, engineering, and the sciences.
• Learn a (programming) language. Learning how to think like a computer is wonderful experience. Some languages, like Prolog and ML, will give you explicit practice in logic; but even a language like C++ will give you valuable lessons in thinking that can be applied in your mathematical career.
• Learn a (human) language. Much of mathematics is about the meanings of specific words, and careful use of language. Understanding a language other than your native language will help you think critically about the words you use.
• REU. A Research Experience for Undergraduates program is a residential summer program (usually about two months long) aimed at training you in a specific research topic and then giving you the opportunity to work (along with other undergraduates) on an open research problem. REUs typically require a year of algebra and analysis, and the application process is in the Spring.
• PUMS. The Penn Undergraduate Math Society is our mathematics club. PUMS sponsors seminar talks, social gatherings, and sometimes problem sessions.