## The Math Major and its Requirements [1]

**Introduction**

The mathematics degree at UMass provides the student with broad exposure to the most important themes in mathematics and statistics, while allowing the student to specialize in one or more areas. Our rigorous mathematical and statistical traIning, coupled with exposure to computing paradigms (whether in Java, Python, MATLAB, R, and/or SAS), has provided our majors with increasing success in the job and graduate school marketplace. In just the past year, primary math majors have taken jobs at companies ranging from British Aerospace to Microsoft to Optum to MassMutual to Willis Towers Watson, have begun Master's programs including at WPI, Northeastern, Harvard, and UMass in a range of fields such as Applied Math, Statistics, Biostatistics, Computer Science, Data Science, Education and Business, and have started PhD programs at UC Berkeley, Michigan, UT Austin, UC Santa Barbara, and Boston University in Pure Math and Biostatistics. Our second majors have used the math degree to amplify their training in such subjects as Economics, Physics, Computer Science, Finance, Engineering, Chemistry and Psychology.

The department offers seven **concentrations [2] **as part of the mathematics degree, which allow the student to specialize in one of six focused areas, or create their own: Actuarial [3], Applied Math [4], Individual, [5] Math Computing [6], Pure Math [7], Statistics [8], and Teaching [9].

For information about joining the major, please see our advising page. [10]

**Core Requirements for all Majors**

**Differential and integral calculus:**Math 131 and 132, with a grade of C or better in Math 132**Multivariable calculus and linear algebra:**Math 233 and 235**Introduction to abstract mathematics:**Math 300 or CompSci 250. This requirement may be waived by the Chief Undergraduate Advisor [10] for students who have taken advanced math coursework elsewhere in abstract algebra, real analysis, or number theory.**Computer programming:**CompSci 121 or equivalent**Writing in mathematics:**Math 370**Integrative Experience (IE) course.**The following courses satisfy the IE requirement: Math 455, Math 456, Math 475, Stat 525, Stat 494CI**.**All IE courses count toward either required major courses or upper level major electives. In other words, this requirement does not require additional coursework to be completed.- Completion of the requirements of one of the following concentrations: Actuarial [3], Applied, [4]Individual [5], Mathematical Computing [6], Pure [7], Statistics [8], Teaching [9].

**Grade Requirements**

- All courses used to satisfy these requirements must be completed with a passing grade (D or higher) and cannot be taken Pass/Fail.
- The overall GPA of all courses taken to satisfy the requirements for the major (averaged over all such courses taken) must be at least 2.0.
- Students will need to
**earn a grade of C or better in Math 132 before taking certain courses at the 300 level or higher**.

**Concentrations and their requirements**

Mathematics majors must choose one of the following **concentrations **before registering for their third semester of classes. Courses from outside the department may be used to satisfy the concentration requirements: a list of accepted University courses is available here [11]. The Chief Undergraduate Advisor may approve other courses taken outside the department or at another university, but this must be done before the student enrolls in them.

### 1) Actuarial Concentration

Actuarial Checklist [12]

The Actuarial Concentration prepares the student for a career in the actuarial sciences. Requirements:

**VEE requirements outside the department**: Econ 103, Econ 104, and Finance 301.**Accounting 221**is now a VEE, but it is not yet a requirement of the concentration.**Probability and statistics**: Stat 515 and Stat 516**Linear Regression:**Stat 525. Stat 525 is an IE course.**Exam preparation**: Math 437 or Math 536**Mathematics of finance**: Math 537- Three of the following courses: Math 331, Math 425, Math 456, Math 523H, Math 545, Math 551, Stat 526, Stat 535, or an appropriate course outside the department such as Finance 422 or Econ 309. For other substitutions, please consult with the CUA. Only one course outside the department is typically permitted.

See the Actuarial Sciences [13] webpage for further details on this concentration.

### 2) Applied Mathematics Concentration

The Applied Mathematics Concentration prepares the student for applied matematics positions in industry or government. Requirements:

**Advanced multivariate calculus:**Math 425**Differential equations:**Math 331**Linear algebra for applied mathematics:**Math 545**Introduction to scientific computing:**Math 551- One of the following courses: Math 456, Math 532, Math 534, Math 552. Math 456 is the IE course for this concentration.
- Three additional courses numbered 400 or higher (
**except Stat 501)**. With the approval of the Chief Undergraduate Advisor, these may be appropriate courses outside the department (popular choices are MIE 379 and Public Health 496).

### 3) Individually Designed Concentration

Individual Checklist [15]

The individually designed concentration permits students, in consultation with the Chief Undergraduate Advisor, to design their own concentration so as to explore a theme in mathematics or statistics or to investigate connections between the mathematical sciences and another field. An individual concentration includes the core requirements above plus eight courses numbered 400 or above, of at least three credits each. In practice, very few students choose this option since most of the other concentrations have enough flexibility, including three open electives in both the Applied Math and Statistics concentrations. Generally, the individual concentration will only be approved for students with a single major to allow them to gain exposure to multiple disciplines, rather than as a mechanism to add a second major in math using coursework from a primary major. Students also have the option to do BDIC [16] if they are interested in a field that utitilizes mathematics, statistics, or data science.

### 4) Mathematical Computing Concentration

Mathematical Computing Checklist [17]

The Mathematical Computing Concentration prepares the student for careers that require both knowledge of advanced mathematics and knowledge of computer science.

Requirements:

**Data Structures:**CompSci 187 or ECE 242. This course is needed as a prerequisite in the sequence of courses leading to CompSci 311.**Abstract algebra:**Math 411**Probability:**Stat 515**Intro Scientific Computing:**Math 551**Algorithms:**CompSci 311- Either CompSci 501, Math 513, or CompSci 575
- Two additional courses from the following list: Math 331, Math 412, Math 456, Math 471, Math 571, Math 545, Math 552 or Stat 516. The IE course on this list is Math 456.
- CS elective: any 300+ level CS course of 3 credits or more that is not used to satisfy any of the previous requirements.

### 5) Pure Mathematics Concentration

Pure Math Checklist [18]

The Pure Mathematics Concentration gives students exposure to the core mathematics subjects and prepares students for graduate study in mathematics. Requirements:

**Abstract algebra:**Math 411**Complex variables:**Math 421**Advanced multivariate calculus or topics in real analysis:**Math 425 or Math 524**Analysis:**Math 523H- Either Math 412 or Math 563H
- 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 - Two additional courses numbered 400 or higher (
**except Stat 501**). Most students will select one of these to be Math 455 to satisfy the IE requirement. With the approval of the Chief Undergraduate Advisor, these may be appropriate courses outside the department.

### 6) Statistics Concentration

Statistics Checklist [19]

The Statistics Concentration prepares the student for a career as a statistician or a data scientist or for graduate study in statistics or biostatistics. Requirements:

**Advanced multivariate calculus:**Math 425**Linear algebra for applied mathematics:**Math 545**Probability and statistics:**Stat 515 and Stat 516- One of the following courses: Stat 525 or Stat 526. The IE course on this list is Stat 525.
- Three additional courses numbered 400 or higher (or Math 331). With the approval of the Chief Undergraduate Advisor, these may be appropriate courses outside the department; a popular choice is Public Health 460.
**Note: Stat 501 cannot be used for this list.**

### 7) Teaching Concentration

Teaching Checklist [20] - For entry Fall 2016 and later

Teaching Checklist [21] - For entry prior to Fall 2016

The Teaching Concentration provides the student with the knowledge of mathematics and statistics required by the Commonwealth for teaching mathematics at the 8-12 level. **The teaching concentration requirements have been updated for students entering the University in Fall 2016. Current students have the option to meet either the requirements listed on their ARR on SPIRE or these new requirements. **

**Abstract algebra:**Math 411**Mathematical modeling:**Math 331 or Math 456**Discrete/finite mathematics:**Math 455 (an IE course)**Geometry:**Math 461**Probability and statistics:**Stat 501 followed by Stat 515**Use of technology:**Math 471- One additional course numbered 400 or higher. (Math 475, History of Math, is recommended since it is a state requirement for secondary teachers).