Planning your courses through the Math-Stat Major

What should be a plan by semester for taking courses to succeed in the math major? There is relevant objective information elsewhere on our Math Majors webpage. Our remarks are a mix of facts and strategy, based on experience, for successfully navigating through the math major requirements and opportunities.

Generalities: There is a great range in our majors. Some aim for grad school, some for secondary education, some for a job after a bachelor's degree. Some are very strong in mathematics, others do not have such great natural talent. Some have no outside commitments; others work 20 hours a week. Many are double majors. There is no path through the major which is best for all students.

As you change and grow during the college years, your aims and circumstances and self-assessment will probably change. It's unlikely they will be the same at the end of your Maryland years as at the beginning. Nevertheless, it is valuable to make some plan for how you might go through the math major. If you think you have a goal and work on a plan to achieve it, then you will achieve it, or discover you want or need to change goals. If you have no plan, you might not confront the reality of your current goal until your options for change become limited.

Math 410: Math 410 is the watershed course for most math majors. There you do serious proofs which give you a true mathematician's understanding and open the door to further work. If you get through Math 410-411 in the junior year (preferably Fall), then you are over the hump in the math major, and in good shape for all the rest. If at all feasible, plan your program to give a good chance of success in Math 410 not later than the end of your junior year.

Math 410 is very challenging, and you should take it with sufficient preparation:

• Students with A's in Math 140,141,240,241 and 246 can generally move directly into Math 410.
• Students with B's and C's in these courses should NOT move directly into Math 410. Generally these students should first take Math 310, a bridge course developed specifically to prepare students for 410 and abstract proof.
• Math 310 will be offered in the summer and this may be a useful option for a student who wants Math 410 in Fall of the junior year.
• If Math 310 does not fit into your schedule, another way to ease the transition into 410 would be an entry-level proof-writing course such as Math 406 or Math 430, with another relatively easy 400-level course such as Stat 400.  In addition, assuming there is sufficient interest, we will also be offering Math 307 in the winter.  Math 307 is a 2-credit condensed version of Math 310.
• Students with A's and B's in Math 140,141,240,241 and 246 are judgment calls regarding the direct move into Math 410.
• Math 410 is our "gateway mathematical maturity course".
  It is generally a bad idea to take Math 403 or Math 405 a semester before Math 410, as a "warmup". These courses should be and generally are of comparable difficulty as serious proof courses. Math 403 also covers material less familiar to the students. If you are not ready to take 410, then your are probably not ready for 403.

Loads

• In your junior and senior year, typically, it is appropriate to include two upper level math courses in a semester, and not more. That is about the pace for finishing in four years. This constraint may vary with the complementary course load, student, nature of the courses, etc. Talented students can take more.
• Roughly, the hardest math undergraduate courses are 410,411,412, 403 and 405. These are serious proof classes. Usually the first of these taken is 410. Except for a really strong student, the complementary math load should be light for the first hard class, and perhaps later.
• On the other hand, a strong straight A student might be fine taking both 403 and 410. Just be careful about such a load. You can discuss with your math advisors what load might be appropriate for you.
• For a typical math major: working more than 10 hours a week part time will tend to interfere with success with a full math major load. Rather than pass this limit, it may be better to borrow more money, get extra help from parents or or reduce the course load.

The high road and the low road: Math major requirements can often be met by various courses. Rule of thumb: students with GPA under 2.8 should usually take the easier or less abstract option.

• Algebra Requirement.
  Math 403 and 405 are hard. Math 401 is easier.
• AMSC Requirement.
  AMSC 460 is less theoretical than AMSC 466. AMSC 460 is the standard choice. Students with a theoretical inclination, especially those thinking of going to graduate school in mathematics or applied mathematics, are encouraged to take AMSC 466.
• Differential equations requirement.
  Almost all our majors satisfy this with Math 246. Only strong math majors should plan to satisfy it with Math 414 (which has a Math 410 prerequisite). Math 436 (Differential Geometry) will satisfy this requirement, but in fact the student will not learn much about differential equations in Math 436.
• Math 411 vs. Math 412.
  The courses are comparable in difficulty and overlap 80-90% in content. Relatively speaking, Math 411 includes more theoretical material and proof, and Math 412 has more analysis of applications and rigorous estimation. A student aiming at graduate school in mathematics should generally take Math 411. If Math 411 is full, though, Math 412 can still work well for such a student, if the student makes arrangements with the professor to cover the missing material (roughly a chapter of the usual text).
• Stat 400-401 vs. Stat 410-420.
  Stat 400 and Stat 401 are introductory probability and statistics (respectively), as are Stat 410 and Stat 420. The latter two are much more theoretical and challenging and include many graduate students.

Graduate School: The program of a student aiming at graduate school in mathematics should include Math 403, 405, 410, 411(or 412 with outside study) and 463. For students aiming at graduate school outside of mathematics, Math 410, 411 and 405 are usually the most valuable. The career center runs workshops on "How to apply for graduate school".

Tracks: There are three tracks through the math major: traditional, education, and statistics.

• Traditional ("low road").
  An example would be MATH 246, 401, 410, 412, 406, 420, STAT 400, STAT 401, AMSC 460.
• Traditional ("high road").
  An example would be MATH 410, 411, 403, 405, 414, AMSC 466 and two graduate classes.
• Education.
  This track is aimed at secondary education/math double majors. These students have extremely crowded schedules and math course requirements which are a bit more lenient.
• Statistics.
  This track is especially aimed at students who want to graduate with a marketable package of skills along with the Bachelor's degree. A strong student aiming at graduate school in statistics should take not only stat courses but also Math 411 or Math 412 (which are not required in the stat track). The core of the usual Stat track is Stat 400, 401, 410, 430 (probability, statistics and data manipulation with SAS).

Example four year plans: The following sample four year plans cover the mathematics major requirements. These plans do not include the general education CORE requirements. There are many variations on these plans.

Traditional Track

Education Track

Statistics Track

Math 340-341 and honors: This is the very high road. A student finishing Math 340-341 in the freshman year is a year ahead and should be a very strong student. An A student in 340-341 should be quite ready for Math 410. We hope a good number of these students go into Math 410-411 in the sophomore year. Then the student will have a lot of freedom, and the potential for extremely strong credentials in applying to graduate school.
Below is one example (among a great many). The key is 410-411 in the sophomore year.

Traditional Track (Dept. Honors)

• Every semester: MATH 310, 401, 402, 403, 405, 406, 410, 411, 430, 452,456, 462, 463,and 464,
  STAT 400, 401, and 410, and  AMSC 460 and 466.

• Fall semester: MATH 414, 424, 431, 432, 436, 450, and STAT 430, 440.
• Spring semester: MATH 404, 412, 437, 446, 475 and STAT 420, 470.

• Summer: MATH 310,401,406,410,411,462,463, STAT 400, and AMSC 460.

AMSC 460/466 prerequisites: Before a student attempts AMSC 460 or 466, he/she should have completed a computer course like CMSC 106, or have obtained similar experience elsewhere. Because these AMSC courses generally use MATLAB, this is a "computational maturity" requirement, but from experience a good one.

Statistics: Employers like students with some statistics. STAT 400 (probability) can be followed by STAT 401 (statistics) and/or STAT 430 (doing statistics on data with SAS). These are particularly good upper level electives for students not headed to grad school. STAT 401 and STAT 430 are offered in spring and fall respectively and STAT 400 is offered every semester.

Special Course Offerings: Don't forget to consider Special Course Offerings. Look for fliers describing these courses in detail.

Graduate Classes: With permission from the undergraduate office and the dean's office, talented undergraduate students may take graduate classes. The undergraduate office will usually not approve graduate classes for a student who has not progressed successfully and with fine grades through most of the major. The dean's office has at times denied a student permission to take a graduate course when the student has not made appropriate progress on CORE requirements.

Miscellany:

• Students may not take any math major requirement off campus. This includes the computer programming requirement and supporting sequence.
• Students may take CORE requirements off campus, with permission of the dean's office.
• Here are some items to consider discussing with the math professor advising you.
  • Course selection for this semester.
  • Course selection for future semesters.
  • Career Plans.
  • Undergraduate Research.
    Research Interactive Teams (RITs) can carry academic credit counting toward the upper level mathematics requirement, and there is a possibility of finanical support from our Undergraduate VIGRE program.
  • Internships.
    See the CMPS Internships Website for more information.