Resources for Math Majors


This page contains resources for undergraduate Math Majors. Here is a list of the topics covered.

  1. Study Tips for Advanced Math Courses
  2. Professional Societies
  3. Undergraduate Research Projects and Other Programs
  4. Advice Regarding Extracurricular Opportunities
  5. Resources for Math Majors Considering Graduate School
  6. Career Resources
  7. Interesting and Fun Math Links



1. Study Tips for Advanced Math Courses

As you proceed in your mathematical education, you will find upper level math courses to be quite a bit different from lower level math courses. (In fact, many math majors do not get a really good understanding of what mathematics is until their junior or senior year of undergraduate studies.) Upper level math courses have greater emphasis on conceptual understanding, abstraction, and the ability to modify known results to deal with new situations.

TRANSITIONING TO ADVANCED COURSES. There are different expectations in upper level courses: You will be expected to read your textbook and do more of the work on your own; you will be expected to write proofs and communicate mathematical ideas and arguments; more time will be spent on conceptual understanding and less time will be spent on computation.

You will start to see these differences a bit in sophomore-level courses (such as a Linear Algebra class or an Introduction to Proofs class), and the differences will be even more pronounced in higher-level courses, where typically much greater emphasis is placed on understanding theorems and writing proofs.

Here are some guides I have written for students making the transition to advanced math courses.


STUDYING ALONE VS. STUDYING IN A GROUP. Research by Uri Treisman at the University of California at Berkeley suggests that students can improve their performance in mathematics classes if they study in groups with group work being a complement to (not a replacement of) individual study. Group work also has the advantage of promoting a blurring of the distinctions between the academic and social spheres of students' lives.

With this in mind, if you want group work to be helpful, you should collaborate with other students in addition to the standard "3 hours of individual studying for each 1 hour in class". If you study with a group in addition to your individual study, it will improve your performance and knowledge of the material. But if you work in groups at the cost of working less on your own, it can hurt your performance.

It is a good idea in each of your courses to form a study group with two to five other students. Get the email address or phone number of the students in your study group. Even if you do not spend much time working with them, they are a useful resource for asking questions or to find out what was missed (and get notes) if absent from a day or two of class.


STUDYING ALL NIGHT. The following is from p.20 of the August 8, 1994 issue of Time magazine:
"Students who think nothing of pulling all-nighters, take note: experiments with both rats and humans have convinced researchers that people who get plenty of sleep are better at learning things. The brain evidently uses its rest periods to consolidate new memories."
Pulling all-nighters to study for finals or other exams, or to complete homework sets or take-home exams, is largely ineffective. The price you pay by losing sleep, and the reduced performance due to exhaustion, far outweigh the benefit of the extra hours of studying. Worse than that, the material you cover during your all-night binge often does not get placed properly into your long-term memory, so you forget it very quickly. This means that if you need the material for subsequent courses or in your future career, pulling an all-nighter is not going to provide you with what you need to know. All-nighters cheat you out of the opportunity to master the material and make it part of your permanent skill set.


PACING YOURSELF. Mathematics is not suitable for cramming. Read the appropriate sections prior to class, take notes during lecture, review your notes and the textbook shortly after the lecture, and begin the assigned problems while the material is fresh in your mind. Do the homework regularly and do a few problems every day; do not do all the problems at once. If you get behind in the homework, doing a bunch of problem sets all at once is often not useful, just as it would not be useful to miss your workouts for a month and then try to train for a 10K run all in one day, or miss your piano lessons for a month and then try to cram for a recital by practicing for hours the day before. When it comes to mathematics homework, you want to work regularly and consistently, much as you do when training for a physical event or learning to play a musical instrument. Your mind needs time to get used to the new ways of thinking and to build mental structures for organizing the material. In fact, research in neuroplasticity has shown that learning certain new skills (including mathematics) actually changes the physical structure of your brain by creating new neural pathways. This kind of change does not occur all at once, and requires repeated practice to develop. Just as building muscle requires regular and consistent physical workouts, building your brain requires regular and consistent mental workouts. Continuing the analogy further: If you don't do enough exercises at one time, it will not add up to a cumulative benefit; and if you do too much at once, you risk fatigue or strain. You need to practice regularly and consistently, at a level where you push but do not strain yourself.


OFFICE HOURS. Make use of your professor's Office Hours. You will find that you get the most out of office hours if your have read the book, attempted the problems, and thought about the material on your own before asking the professor. Come prepared and ask specific questions. For more details, see my advice on office hours for undergraduates.


THE IMPORTANCE OF READING YOUR TEXTBOOK. As you continue in your mathematics education, it becomes increasingly important that you engage with your textbook as you study and learn. Not all relevant material will be covered in class, and textbooks can provide additional opportunities for motivation, examples, and details beyond what you will encounter in lecture. Furthermore, in upper-level math classes it is a good idea to use additional books to supplement the textbook used in the class, so that you can see multiple perspectives on the subject and be exposed to additional topics that may not be covered in your own text. Finally, it is likely that you will want to learn topics that you have not have a class on, and it is useful to use a handful of texts on the subject to do this. The following are some suggestions for textbooks on particular topics.

Textbook Recommendations for Self Study



2. Professional Societies

There are several professional societies for mathematicians. The two main professional societies are the following:
Sometimes the differences between the AMS and MAA are summarized as "The MAA is more concerned with mathematics education, while the AMS is aimed more at professional mathematicians". While there is some truth in this, it is a crude oversimplification of the much more subtle differences that exist. The AMS and MAA are both interested in mathematics education at all levels as well as research mathematics, but their missions place different emphasis on various issues within education and research.

As a mathematics student, you should consider joining both the AMS and MAA. Membership information can be found on each society's website, and you should be aware that the student rates for membership are much cheaper than rates for faculty. As a member of a professional society, you receive the monthly publications of the society, discounts on books and conference registrations through that society, mathematics and society news, information about mathematics opportunities, and access to certain online information. Your membership also supports the mathematics community and shows a level of professionalism that future employers and graduate programs like to see.

In addition to the AMS and MAA, there are other popular professional societies in mathematics with more specialized roles:
Even if you are not a member of a particular society, their website can often be a source of very useful information for you. In particular, the AMS and MAA both have a list of resources or undergraduate mathematics majors on on their websites, and these are accessible to everyone.




3. Undergraduate Research Projects and Other Programs for Math Majors

An important way to enhance your undergraduate mathematics education is through participation in an undergraduate research project or long-term mathematics program at another university.

If you are interested in doing an Undergraduate Research Project with a professor in your own department, please see the following page for advice: If you are interested in doing an Undergraduate Research Project at another university or participating in some other kind of Mathematics Program, see the following pages.


4. Advice Regarding Extracurricular Opportunities

Every undergraduate should be involved in some kind of extracurricular activity related to their major.

Extracurricular activities often provide great experiences for students involved in them. They give you the chance to learn more about your profession, gain experience for your future career, and learn about aspects of your major that you do not see in the classroom. They also provide wonderful networking opportunities and chances to develop collaboration or leadership skills.

On top of all these wonderful reasons, there is also a more practical aspect to being involved in extracurricular activities. A college degree is not a ticket to a career. The fact of the matter is that if you graduate and your resume says nothing but B.A. or B.S. in your field of study without a single additional activity relevant to your career path, then its unlikely you will get a job or get accepted to graduate school. A degree is considered a baseline requirement for most careers --- it is one necessary part, but it is not sufficient by itself.

In a competitive job market, with lots of people coming out of college with degrees in your subject, you need additional activities, involvements, and experiences to make yourself marketable. You need to do something to distinguish yourself. You need to show an interest in your field and a commitment to it that displays more than just satisfying the minimum requirements. If you don't do these additional things, there are plenty of other people out there who are, and you will probably be passed over in favor of them. In fact, when you see individuals who graduate from college with a degree, perhaps even with a good GPA to go with it, but are now unemployed or working a minimum wage job, it is often the case that they did nothing beyond the basics in earning their degree. Employers and graduate schools are interested in individuals who are active, accomplished, and passionate. One way to communicate these qualities is through your choice of extracurricular activities.

Every Math Major should be involved in some kind of activity beyond just their coursework. Possible activities include being involved in your depart's undergraduate math club, attending talks at a department colloquium, serving as a mathematics tutor at your school's tutoring center, and joining professional societies such as the AMS and MAA. Furthermore, every Math Major (and especially those planning on graduate school) should give some serious consideration to being involved in an Undergraduate Research Project and participating in at least one Mathematics Program outside of their own college or university.




5. Resources for Math Majors Considering Graduate School


The AMS and MAA maintains a lists of links to resources for students considering graduate school in Mathematics.

Deciding if You Want to Go to Graduate School

Here is some information to learn more about what graduate school entails and help you decide if it is for you. Some useful information to know:

Preparing for Graduate School



Choosing a Graduate School



Applying to Graduate Schools

The following contain various tips on things you should do when applying to graduate school and this article describes some things you should avoid:

Fellowships for Graduate Schools

Although you typically do not have to pay to attend a Ph.D. program in mathematics, you may still want to apply for a graduate fellowship to fund your education. Graduate Fellowships will pay for your education for a number of years, and hence during this time you will not have to TA, which frees up numerous hours per week for studying and research. In fact, many of them pay more lucratively than a TA position, so if you have one you will also have more income than you would while working a TA position. In addition, most graduate fellowships are highly prestigious, and receiving one is something you can put on your Resume/Curriculum Vitae, which will help you get a job after graduate school.
Here is a list of Graduate Fellowships.


6. Career Resources

Math is used in so many different careers that it is difficult to provide a list covering all the possibilities. Take a look at the following links to get an idea of all the different kinds of career options that are available.


7. Interesting and Fun Math Links







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