### Learning Outcomes

Upon graduation from Dickinson, Mathematics majors will be able to:

- employ discrete and continuous methods to solve problems requiring a breadth of knowledge of core mathematics concepts;
- implement a variety of logical techniques to construct or assess the validity of a mathematical argument;
- communicate mathematics clearly and accurately both orally and in writing to mathematical audiences.

### Major

11 courses

170, 171, 211, 262, 270, 351, 361

One math course having 351 or 361 as a prerequisite

One additional math course numbered 301 or higher

Two additional math courses numbered 201 or higher. One of these courses may be replaced by COMP 132 or ECON 398 or, upon prior approval by the department, a mathematics-intensive course from another department.

### Minor

Five courses

171 and 211, one of the three courses 325, 351 or 361 and two other courses numbered 201 or higher.

Possible tracks include:

Track 1: 170, 171, 211, 262, 270, 361

Track 2: 170, 171, 211, 262, 351, elective

Tracks 1 and 2 focus on theoretical mathematics.

Track 3: 170, 171, 211, 225, 325, elective

Track 3 focuses on statistics.

### Suggested curricular flow through the major

There are many possible paths through the mathematics major. Which path to take depends on the student’s prior coursework and placement. We present four models here. With careful planning, all four models allow the possibility for students to spend a semester or a year abroad.

**Model 1** - MATH 151 as entry point (for students who place into 151)

*First Year:* 151, 170

*Sophomore Year:* 171, 211, 270, 262

*Junior and Senior Years:* 351, 361, MATH electives

**Model 2** - MATH 170 as entry point (for students with suitable pre-calculus preparation)

*First Year:* 170, 171

*Sophomore Year:* 211, 262, 270

*Junior and Senior Years:* 351, 361, MATH electives

**Model 3** - MATH 171 as entry point (for students with 170 credit)

*First Year: *171, 270

*Sophomore Year:* 211, 262

*Junior and Senior Years: *351, 361, MATH electives

**Model 4** - MATH 171 as entry point (for students with 170 and 270 credits)

*First Year *[Option 1]: 171, 211

*First Year* [Option 2]: 211, 262

*Sophomore Year* [Option 1]: 262, MATH elective

*Sophomore Year *[Option 2]: 171, MATH elective

*Junior and Senior Years:* 351, 361, MATH electives

Students who are interested in applied mathematics should consider the electives 225, 241, 325, and 331 during their third and fourth years.

**Note: Mathematics and Computer Science are one department but have been filed individually and alphabetically for ease of access.**

**MAJOR ADVISORS**

A student wishing to declare a major should contact the department chair; detailed instructions for declaring a Mathematics major are available on a separate page. Based on the student’s preferences and interests and current faculty advising loads, the chair will assign one of the department faculty as the major advisor. Students are encouraged to meet with their major advisor at least once per term prior to course selection to discuss directions of study and how they align with future goals and plans.

### Honors

Departmental honors is the highest distinction that the Department can award to a Major. Majors who receive departmental honors will be those who demonstrate a broad mastery of the discipline as well as an ability to complete and present high quality research. A broad mastery of the discipline is demonstrated by a GPA of 3.40 or higher in all courses related to the major. The ability to complete high quality research is demonstrated by the completion of a yearlong research project. This project will be characterized by an independent and in-depth study of an advanced topic including a literature search, reading of original sources and a novel formulation of results. Finally, the ability to present such research is demonstrated by the preparation of an honors thesis, a public presentation and a successful defense of the work to the department faculty. Detailed guidelines can be found on the departmental web page.

### Co-curricular activities/programs

The Math and Computer Science Society is a student-run club that organizes academic and social events in the department. In a typical year they host several departmental coffees, an ice cream social, a Pi-day event, game nights, happy hours and often a trip to a site of interest in a nearby city (Washington, Baltimore, New York, Philadelphia).

The department runs the Math/CS Chats: a colloquium series, in which speakers (faculty, alumni and other guests) give talks of academic interest to majors in mathematics and computer science. These talks typically occur over the lunch hour and pizza is provided.

### Courses

121 Elementary Statistics

An introduction to the science of collecting, organizing, analyzing, and interpreting data. The focus is on data presentation and statistical reasoning based upon the analysis of data sets. Topics include the study of sampling methods, observational and experimental studies, graphical and numerical summaries of data, probability, sampling distributions, significance testing, estimation, and simple linear regression. Does not count toward the major or minor in mathematics.*Students cannot take this course concurrently with 225. Students who have received credit for 225 cannot take this course for credit. Offered every semester. *

Attributes: ARCH Area A Elective, ARCH Area B Elective, Appropriate for First-Year, ENST Foundations (ESFN), LPPM Empirical Social Analysis, Quantitative Reasoning

151 Introduction to Calculus

An introduction to limits and derivatives together with a review of polynomial, rational, trigonometric, exponential, and logarithmic functions.
*Three hours of classroom and one and a half hour of lab per week. Prerequisite: departmental placement. Students who have received credit for MATH 170 cannot take this course for credit. Offered every semester.*

Attributes: Appropriate for First-Year, ENST Foundations (ESFN), Quantitative Reasoning

170 Single Variable Calculus

The study of real-valued functions, including transcendental functions, limits, derivatives and their applications, the definition of the Riemann integral, and the Fundamental Theorem of Calculus.*Three hours of classroom and one and a half hour of lab per week. Prerequisite: 151 or departmental placement. Offered every semester.*

Attributes: Appropriate for First-Year, ENST Foundations (ESFN), Quantitative Reasoning

171 Multivariable Calculus

Multivariable calculus including parametric and polar equations, vectors, three-dimensional analytic geometry, vector-valued functions, functions of several variables, partial derivatives, and multiple integrals. Additional topics if time permits.*Three hours of classroom and one and a half hour of lab per week. Prerequisite: 170 or departmental placement. Offered every semester. *

Attributes: Appropriate for First-Year, ENST Foundations (ESFN)

180 Introduction to Data Science

An introduction to the principles and tools of data science focusing on exploratory data analysis. Topics include types of variables, mathematical representations of data, data wrangling and transformations, data visualization and numerical summaries, and supervised and unsupervised machine learning. The course includes an introduction to the R statistical programming language.*Prerequisites: MATH 170 or department placement. This course is cross-listed as COMP 180 and DATA 180. Offered every semester. *

Attributes: Appropriate for First-Year, ENST Foundations (ESFN)

201 Special Topics

Topics to be announced when offered.

*Prerequisite: permission of the instructor. One-half or one course credit.*

202 Special Topics

Topics to be announced when offered.

*Prerequisite: permission of the instructor. One-half or one course credit.*

211 Foundations of Higher Mathematics

An introduction to fundamental mathematical concepts used in mathematics and computer science, with an emphasis on writing mathematical arguments. The course presents the principles of mathematical logic, sets, functions, and methods of proof. *Prerequisite: 170 or COMP 130 or departmental placement. Offered every semester.*

Attributes: Appropriate for First-Year, ENST Foundations (ESFN), Writing in the Discipline

225 Probability and Statistics I

A calculus-based introduction to the core topics of probability and statistics. Topics include discrete and continuous random variables, joint distributions, expectation, variance, random sampling from populations, hypothesis tests, and confidence intervals. The course includes an introduction to the R statistical programming language. *Prerequisite: 171. Offered every semester.*

Attributes: ARCH Area A Elective, ARCH Area B Elective, ENST Foundations (ESFN)

241 Computational Mathematics

An introduction to a broad range of numerical methods for solving mathematical problems that arise in science and engineering. Focus is given to developing a basic understanding of numerical algorithms, their applicability, and their limitations. Topics typically include floating-point number representation, sources of error, conditioning and numerical stability, root finding, solutions of both linear and nonlinear systems, least squares, splines and polynomial interpolation, optimization, and numerical differentiation and integration. The implementation and validation of algorithms through computer programming is also emphasized. No prior programming experience is required.*Prerequisite: Completion of two of the following courses: 170, 171, 211 and 270. This course is cross-listed as COMP 241. Offered in even numbered spring semesters.*

Attributes: ENST Foundations (ESFN)

262 Linear Algebra

An introduction to matrix algebra and abstract vector spaces with an emphasis on writing mathematical arguments. Topics include linear systems and matrices, vector spaces, linear independence, eigenvalues and eigenvectors.*Prerequisite: 211 or permission of the instructor. Offered every semester.*

Attributes: ENST Foundations (ESFN)

270 Integration and Infinite Series

The study of methods of integration, applications of the integral, elementary differential equations, and infinite sequences and series.*Prerequisite: 171 or departmental placement. Offered every spring. *

Attributes: Appropriate for First-Year, ENST Foundations (ESFN)

271 Differential Equations

Elementary methods of solutions of selected types of differential equations; solutions of systems of linear differential equations with constant coefficients; and a brief introduction to numerical methods and nonlinear systems. Includes a strong emphasis on applications. *Prerequisite: 171 and 270. Offered in odd numbered fall semesters.*

Attributes: ENST Foundations (ESFN)

301 Special Topics

Topics to be announced when offered.*Prerequisite dependent upon topic. One-half or one course credit. *

302 Special Topics

Topics to be announced when offered.*Prerequisite dependent upon topic. One-half or one course credit. *

311 Applied Combinatorics

An advanced course in discrete mathematics introducing the basic tools of combinatorics and their applications. The course will consider the three basic problems of combinatorics: counting, existence and optimization. *Prerequisite: 211. Offered even numbered spring semesters.*

314 Computability and Complexity

An introduction to the theory of computation, addressing the fundamental question of what problems can be solved using computers, both in principle and when efficiency is taken into account. Topics may include: finite automata, undecidable problems (such as the halting problem), Turing machines, regular languages, context-free grammars, universal computation, elementary complexity classes, NP-completeness, and the P vs NP problem.

* Prerequisite: COMP 132 and MATH 211. This course is cross-listed as COMP 314. Offered every spring.*

325 Probability and Statistics II

A continuation of Introduction to Probability and Statistics I. Topics include additional discrete and continuous distributions, conditional distributions, moment generating functions, additional hypothesis tests, simple linear regression and correlation, multiple linear regression, and analysis of variance. The course expands proficiency in the R statistical programming language. *Prerequisites: 171 and 225. Offered every semester.*

Attributes: ENST Foundations (ESFN), Quantitative Econ Elective

331 Operations Research

An introduction to deterministic operations research, including linear programming, sensitivity analysis, and duality. Special topics may include transportation and assignment problems, network models, integer programming, and game theory.*Prerequisite: 262. This course is cross-listed as COMP 331. Offered in odd numbered fall semesters.*

Attributes: ENST Foundations (ESFN)

351 Abstract Algebra

An introduction to axiomatic formalism using algebraic structures as paradigms. Topics chosen from groups, rings, and fields. *Prerequisite: 262. Offered every spring.*

361 Real Analysis

A theoretical development of the basic ideas and concepts of real analysis. Topics include a study of real numbers, sequences, limits and continuity, differentiation and integration. Optional topics include infinite series, sequences and series of functions, and an introduction to point-set topology.*Prerequisite: 171, 262 and 270. Offered every fall.*

Attributes: Quantitative Econ Elective

401 Special Topics

Topics to be announced when offered.*Prerequisite dependent upon topic. One-half or one course credit.*

402 Special Topics

Topics to be announced when offered.*Prerequisite dependent upon topic. One-half or one course credit.*

472 Complex Analysis

An introductory study of functions in the complex plane. Topics include: complex numbers and functions, the theory of differentiation and integration of complex functions; Cauchy's integral theorem; the Residue theorem. *Prerequisite: 361 and completion of, or concurrent registration in 351. Offered in odd numbered spring semesters.*

481 Topology

An elementary study of topological spaces. Topics include open and closed sets, the Hausdorff property, compactness, connectedness, continuity, homeomorphisms, product spaces, identification spaces, the Euler characteristic, the classification of spaces, and an introduction to the fundamental group. *Prerequisite: 361 and completion of, or concurrent registration in 351. Offered in even numbered spring semesters. *