Students arrange a major in mathematics by developing an Individualized Mathematics Proposal (IMAP). An IMaP outlines a complete, coherent program of study consistent with the goals of the individual student. The courses included in a student’s IMaP are determined after consultation with an MSCS faculty member and approved by the department chair.

A path through the major as described by a student’s IMaP normally includes two semesters of calculus, one semester of linear algebra, and at least seven intermediate or advanced mathematics courses. The intermediate courses should include two transition courses (from among Math 244, Math 252, and Math 242) and courses from at least three different mathematical perspectives (computation/modeling, continuous/analytic, discrete/combinatorial, axiomatic/algebraic). Students must take at least two Level III courses, at least one of which must be part of a designated Level II–Level III sequence.

An IMaP may include up to two related courses from Statistics or Computer Science; a current listing of such courses is available on the mathematics web page. A student may also find a course outside of MSCS that contributes significantly to a mathematical path of study and may petition to have the course included in his or her IMaP.

Here are some possible paths through the mathematics major. These are not suggestions, just food for thought. Consult with a mathematics faculty member about creating an IMaP and the best possible path through the major for you.

- For students beginning in Calculus 1
- First year: Calculus 1 and Calculus 2
- Sophomore year: Linear Algebra in Semester 1, Number Theory in Budapest during Interim, and another 200-level elective in Semester 2
- Junior year: Two transition courses and an elective
- Senior year: Two or more 300-level courses

- For students beginning in Calculus 2
- First year: Calculus 2 and Linear Algebra
- Sophomore year: a 200-level elective in Semester 1, Number Theory in Budapest during Interim, a transition course in Semester 2
- Junior year: Another transition course and a 200- or 300-level elective
- Senior year: Two or more 300-level courses

- For students beginning in Linear Algebra
- First year: Two 200-level electives
- Sophomore year: Two transition courses
- Junior and Senior years: Lots of 200- and 300-level electives

- For students also majoring in Physics
- The Physics major requires Calculus 1, Calculus 2, Linear Algebra, Multivariable Calculus, and Differential Equations
- It is also recommended that physics majors take Complex Analysis and Differential Equations II
- Along with the 7 courses listed above, a student can double major in physics and mathematics by completing two transition courses

- For students also completing a Statistics concentration
- Up to two Stats courses can count toward both a mathematics major and a statistics concentration.

- For students planning to earn secondary school teaching licensure
- Required Math courses: Calculus 1, Calculus 2, Discrete Mathematics*, Linear Algebra, Real Analysis I, Abstract Algebra I, Probability, Geometry
- Required Stats courses: either Statistics for Sciences or Statistical Theory
- *Discrete Mathematics may be replaced with the Computer Science course Mathematical Foundations of Computing. These are offered in alternate years.

## Areas of emphasis

The mathematics major does not have different tracks, but by designing an Individualized Mathematics Program (IMaP) with the help of a mathematics faculty member, students can complete their majors in a variety of ways. Here are some popular area of emphasis:

#### Pure Mathematics

Students intending to earn higher degrees in theoretical mathematics should take a broad range of 200-level courses and as many 300-level courses as possible. At the 200-level, the “transition” courses Real Analysis I (Math 244) and Abstract Algebra I (Math 252) are a must. A variety of courses with different perspectives will provide excellent breadth of knowledge. Advanced courses in Real Analysis II (Math 344) and Abstract Algebra II (Math 352) are also a must. Courses in Topology (Math 348), Combinatorics (Math 364), and Complex Analysis (Math 340) are highly recommended. Students should be alert to special topics courses and independent study & research opportunities. More and more graduate programs expect their successful applicants to have had an undergraduate research experience. Students should strive to achieve good scores on the general and mathematics GRE exams.

#### Applied Mathematics

Students intending to earn higher degrees in applied mathematics should take a broad range of 100- and 200-level courses in mathematics, statistics, computer science and other fields, and as many 300-level courses as possible. At the 200-level, mathematics courses such as Multivariable Calculus (Math 226), Differential Equations (Math 230), Real Analysis I (Math 244), Modern Computational Mathematics (Math 242), Probability (Math 262), and Operations Research (Math 266) teach material that is used in a wide variety of applications to the biological, physical, and social sciences. Advanced mathematics courses in Differential Equations II (Math 330), Complex Analysis (Math 340), Real Analysis II (Math 344), and Mathematics Practicum (Math 390) are highly recommended. Students should be alert to special topics courses and independent study & research opportunities. More and more graduate programs expect their successful applicants to have had an undergraduate research experience. Students should strive to achieve good scores on the general and mathematics GRE exams.

#### Secondary School Teaching

Students planning to teach secondary school mathematics complete a standard mathematics major (with certain courses prescribed by state certification requirements). In addition, they take several courses in the Department of Education and devote part of one senior semester to student teaching.

#### General Mathematics Major

Many mathematics majors do not enter graduate school, law school, business school, or medical school right away or even at all. For those students a broad and deep mathematics major can serve them well in a variety of settings: business, technology, the non-profit sector, consulting, actuarial work, etc. Search the alumni directory for mathematics majors and see the kind of professions Oles have entered.

#### Double Majoring

Many students combine mathematics with another major or concentration. Doubling with majors in the sciences and economics is especially common, as is combining mathematics with a statistics concentration. We also graduate a fair number of students who major in religion, philosophy, art, English, theater, etc. as well as mathematics.