UMass Amherst
Department of Mathematics and Statistics
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Departmental Graduation Requirements for Mathematics Majors

The requirements for a mathematics degree provide the student with maximum flexibility in designing an overall course of study to meet his or her scientific, educational and career goals. The beginning courses emphasize computational skills, problem solving, and the understanding of basic concepts. As students progress, they must solve problems that are less and less routine and more abstract or intricate. Some upper-level courses emphasize proofs and the understanding of abstract structures, while others emphasize advanced computational methods or the formulation and analysis of mathematical or statistical models of reality. A number of the courses involve the use of computers in a fundamental manner in the development of the material covered.

Specific requirements for a major in mathematics are given below. All courses used to satisfy these requirements must be completed with a passing grade, but not with a P. A cumulative quality point average of 2.00 is required in all Mathematics and Statistics courses taken.

  1. Differential and integral calculus: Math 131 and 132
  2. Multivariable calculus and linear algebra: Math 233 and 235/6 or Math 245 and 246
  3. Introduction to abstract mathematics: Math 300 or CompSci 250 (may be waived by the Chief Undergraduate Advisor for exceptionally well-prepared students)
  4. Computer programming: Math 236 or CompSci 121 or equivalent
  5. Writing in mathematics: Math 370
  6. Completion of the requirements of one of the following concentrations: Applied, General, Individual, Mathematical Computing, Pure, Statistics, Teaching. At most four of the courses used to satisfy the concentration requirements may be taken outside the Department of Mathematics and Statistics. The Chief Undergraduate Advisor must approve all such courses taken outside the Department. The grades earned in the courses that satisfy the concentration requirement must average C or higher.

Note that the sequence Math 245-246 may be used to replace Math 233, 235, and 331 in these requirements. In addition, Stat 501 may not be applied to requirements if it is taken after Stat 515 or Stat 516.

Concentrations

Mathematics majors must choose one of the following concentrations.

Applied Mathematics Concentration

The Applied Mathematics Concentration prepares the student for a career as a mathematician in government or industry. Requirements:

  1. Advanced calculus: Math 425
  2. Differential equations: Math 331
  3. Linear algebra for applied mathematics: Math 545
  4. Introduction to scientific computing: Math 551
  5. At least one of the following courses: Math 456, Math 532, Math 534, Math 552.
  6. At least three additional courses numbered 400 or higher. With the approval of the Chief Undergraduate Advisor, these may be appropriate courses outside the department.

General Mathematics Concentration

The General Mathematics Concentration provides the student with broad training in abstract mathematics, statistics, and computing. Requirements:

  1. Algebra: Math 411 or 511 and one of Math 412, 471, 512, 545
  2. Statistics: Stat 515 and 516
  3. Analysis: Math 425 and 523
  4. Scientific Computing: Math 551 and 552

Individually Designed Concentration

Individually designed concentration permits students, in consultation with their academic advisor, to design their own concentration so as to explore thoroughly a theme in mathematics or statistics or to investigate connections between mathematics and/or statistics and another field, such as biology or economics. An individual concentration must include eight courses numbered 400 or above, of at least three credits each. At least four of these eight courses must be in mathematics or statistics. In consultation with their academic advisor, students propose a plan for the eight courses to be used to fulfill the requirements of the individual concentration. No later than the end of the semester in which students are taking Math 300 or during the second semester of the students' sophomore year, whichever comes first, students will: prepare the plan in writing, secure approval of the plan by their advisor, and submit the written plan for approval to the Chief Undergraduate Advisor. No later than the end of the junior year, students review the plan with their academic advisor. If any changes are proposed to the original plan, students must again secure approval of the revised plan in writing.

Mathematical Computing Concentration

The Mathematical Computing Concentration prepares the student for careers that require both knowledge of advanced mathematics and extensive knowledge of computer programming. Requirements:

  1. Computer programming: CompSci 121, CompSci 187, and CompSci 250 or Math 455
  2. Two courses that focus on programming: CompSci 287 and CompSci 311 or on theory: CompSci 401 and Math 513/CompSci 575
  3. Three courses chosen from the following: CompSci 401, Math 411 or Math 511, Math 412 or Math 512, Math 471, Math 513/CompSci 575, Math 551, Math 552, Stat 515, Stat 516.
  4. At least two additional courses numbered 400 or higher. With the approval of the Chief Undergraduate Advisor, these may be appropriate courses outside the department.

Pure Mathematics Concentration

The Pure Mathematics Concentration prepares the student for graduate study in mathematics. Requirements:

  1. Algebra: Math 411 or Math 511
  2. Complex variables: Math 421
  3. Advanced multivariate calculus: Math 425
  4. Analysis: Math 523
  5. At least one of the following courses: Math 412, Math 512, Math 563
  6. At least one applied mathematics course either chosen from the following list or another course with sufficient applied mathematical content approved by the Chief Undergraduate Advisor: Math 331, Math 456, Math 532, Math 534, Math 551, Math 552, Stat 516
  7. At least two additional courses numbered 400 or higher. With the approval of the Chief Undergraduate Advisor, these may be appropriate courses outside the department.

Statistics Concentration

The Statistics Concentration prepares the student for a career as an applied statistician or for graduate study in statistics. Requirements:

  1. Advanced multivariable calculus: Math 425
  2. Algebra: Math 545 or Math 411 or Math 511
  3. Introduction to statistics: Stat 515 and Stat 516
  4. At least one of the following courses: Stat 505, Stat 506, Stat 511
  5. At least three additional courses numbered 400 or higher. With the approval of the Chief Undergraduate Advisor, these may be appropriate courses outside the department.

Teaching Concentration

The Teaching Concentration provides the student with the knowledge of mathematics and statistics required by the Commonwealth as an 8-12 teacher of mathematics. Requirements:

  1. Abstract Algebra: Math 411
  2. Mathematical Modeling: Math 456
  3. Discrete/finite mathematics: Math 112, 119 or 455
  4. Geometry: Math 461 and 462
  5. Probability and Statistics: Stat 501 followed by Stat 515
  6. Use of technology: Math 236, Math 503 or Math 551 (Since Math 236 and Math 503 are no longer being offered, in order to fulfill the requirements of the teaching concentration, the student may substitute another course in the Department that has a substantial computer component for this requirement. Each semester, the Chief Undergraduate Advisor will publish a list of such substitute courses. Past examples of such courses have been Math 471 and Math 532.)




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