# Concentration Information

### The Applied Math Concentration Requirements: 14-15 courses.

### a. Foundation

Two to five courses in calculus and linear algebra (see Notes, part d):

i. Mathematics Ma/Mb, Mathematics 1a

ii. Mathematics 1b

iii. Applied Mathematics 21a, Mathematics 21a, 23b, 25b, or 55b.

iv. Applied Mathematics 21b, Mathematics 21b, 23a, 25a, or 55a

### b. Breadth

Five to seven courses (see item 1.d.i, below) from the following categories. Students must take courses from at least 5 of the 8 categories listed below. Of those, students must take at least one course in Computation and one course in Probability and Statistics. In addition, students must take a course drawn from at least one “continuous” category (Differential Equations or Analysis) and one drawn from at least one “discrete” category (Algebra, Optimization, or Discrete Mathematics). Students must show evidence of satisfying prerequisites for a course to count towards the concentration.

a. Computation: First course: Applied Mathematics 111 and/or Computer Science 50.

Additional courses: Applied Mathematics 205, 207; Computer Science 51, 61, 109a, 109b, 181, 182, 205

b. Probability and Statistics: First course: either Statistics 110 or Mathematics 154, but not both.

Additional courses: Statistics 111, 139, 171, other courses above 110; Mathematics 117; Applied Mathematics 126

c. Differential Equations: Applied Mathematics 105, 108, 202; Mathematics 110

d. Analysis: Applied Mathematics 104, 201, 202; Mathematics 112, 113, 114, 115, 118r

e. Algebra: Linear Algebra: Applied Mathematics 120, Mathematics 121

Abstract Algebra: Applied Mathematics 106/206; Mathematics 122, 123, 124

f. Optimization: Applied Mathematics 121; Mathematics 116

g. Discrete Mathematics: Applied Mathematics 107; Mathematics 152, 155r; Computer Science 121, 124, 125

h. Modeling: Applied Mathematics 50, 91r, 115; Economics 985; or an approved advanced technical elective from outside of the student’s application area

*Remarks:* For AM/Ec students, we usually recommend real analysis (Math 112) and either AM121 or Math 116. The latter two classes cover optimization with different perspectives.

### c. Application

Five courses from an area of application in which mathematics has been substantively applied, selected to provide a coherent and cumulative introduction to mathematically-oriented aspects of the field. See Areas of Application for sample five-course plans.

### d. Notes

i. Five Foundation courses and five Breadth courses are required for students starting in Mathematics M.

ii. Four Foundation and six Breadth courses are required for students starting in Mathematics 1a.

iii. Three foundation and six Breadth courses are required for students starting in Mathematics 1b.

iv. Two Foundation and seven Breadth courses are required for students starting in Applied Mathematics 21a, Mathematics 21a, 23a, 25a, or 55a. Students starting in 21a may take two foundation and seven breadth courses, or may choose to take Mathematics 101 (or 102) as a third Foundation course (if taken in the freshman or sophomore year). If choosing a third foundation course, these students are then required to take only six courses in the Breadth category.

### Petition Form

For any course petitions related to concentration requirements, the Student Course Petition Form should be submitted to the ADUS.

### English Honors

Recommendations for honors are based on the grade point average of the final program of study, the rigor of the overall record, and the satisfaction of the honors modeling requirement. The Committee on Undergraduate Studies in Applied Mathematics votes the level of English honors to be recommended (Honors, High Honors, Highest Honors). To be eligible for English honors, all students must satisfy an honors modeling requirement, in which a paper is written where mathematical analysis is used to understand some aspect of the world around us. The honors modeling requirement can be satisfied in three ways:

- Writing a senior thesis, and turning it in, automatically satisfies the honors modeling requirement for English honors. However, it does not automatically satisfy the Breadth modeling section (v) of the plan of study. Most students who write senior theses register for one semester of Applied Mathematics 91r, which satisfies Breadth section (v) of the plan of study.
**Applied Mathematics 99r cannot be used for Breadth section (v) of the plan of study, since this course is not letter-graded.** - Taking the honors modeling course, Applied Mathematics 115. The last third of this class is spent working on an independent project. A grade of B- or above automatically satisfies the honors modeling requirement.
- A project, undertaken in AM 91r, in which a mathematical analysis of a problem is undertaken. Papers describing the project must be turned in to the concentration, via AM advising, for evaluation by the end of the final exam period in the semester in which the 91r is undertaken.

Recommendations for honors are based primarily on the grades and rigor of the courses in a student's final program of study, and the evaluation of the thesis.

Students who satisfy the modeling requirement without a thesis are eligible for Honors. The GPA cutoff for Honors is 3.5.

A thesis is required for High or Highest honors. There are no set GPA cutoffs for High and Highest honors. In any given year, final GPA cutoffs will depend on the rigor of the eligible students' programs of study. A student's level of honors will be determined by these cutoffs and the quality of their thesis.

### A.B./S.M. Option

Students with sufficient advanced placement credit to qualify for advanced standing may graduate with a bachelor’s and master’s degree in four years. Any student considering this option should discuss requirements with our Office of Academic Programs (Pierce 110) or with the Concentration Advisors.

### Secondary Field

The secondary field in Mathematical Sciences is jointly sponsored by the the Mathematics Department and the Applied Mathematics concentration. Students are required to take four courses in either Mathematics, Applied Mathematics, or Statistics of which at most two can be in Statistics. The Mathematics and Applied Mathematics courses must be numbered 104 or higher; Statistics courses must be numbered 110 or higher.