## Overview

Overview

Students must complete or demonstrate the following before declaring a major in Mathematics:

1. A letter of interest sent to the Mathematics Program Director.
2. One of the following:
1. A grade of A in MAT 130, Precalculus, or
2. A grade of B or higher in MAT 150, Calculus I, or
3. A grade of C or higher in MAT 205, Calculus II.
3. A cumulative grade point average of 2.5 or higher.
4. A letter of recommendation from one of the student’s mathematics instructors. This letter is to focus on the student’s creativity and potential for thriving as a mathematics major.

The Bachelor of Arts degree in Mathematics provides students with a foundation in mathematics and statistics, preparing them for a wide range of career and educational opportunities.

## Courses & Requirements

Summary of Requirements

 2022-2023 Core Curriculum 43 Pre-Major Courses 1 Major and Related Courses 45-48 Free Elective Courses 28-31 TOTAL 120

Required pre-major course 4 hours

MAT 130: Three hours count toward the general studies requirement, replacing GSR 104

To be taken during freshman year:

This course emphasizes the meaning and application of the concepts of functions. It covers polynomial, rational, exponential, logarithmic and trigonometric functions and their graphs, trigonometric identities. Passing both MAT 125 and 126 is equivalent to passing MAT 130.

Required mathematics courses 39-42 hours

MAT 451: EDU 648 may be substituted for MAT 451.

Limit processes, including the concepts of limits, continuity, differentiation, the natural logarithm and exponential functions, and integration of functions. Applications to physical problems will be discussed.

Applications of integration, inverse functions, and hyperbolic functions. Techniques of integration, sequences, series of numbers and functions, and Taylor series.

Vectors, partial derivatives, multiple integrals, line integrals, Green's Theorem, the Divergence Theorem, and Stokes Theorem. Applications to physical problems will be given.

A study of functional principles and proof techniques. Topics will include statements, consequence, proof, sufficient and necessary conditions, contraposition, induction, sets, relations, functions, cardinality, divisibility, prime numbers, congruence, Fermat's Theorem, counting principles, permutations, variations, combinations, binomial coefficients, graphs, planar and directed graphs, and graph coloring.

This course covers the fundamental concepts of vector spaces, linear transformations, systems of linear equations, and matrix algebra from a theoretical and a practical point of view. Results will be illustrated by mathematical and physical examples. Important algebraic (e.g., determinants and eigenvalues), geometric (e.g., orthogonality and the Spectral Theorem), and computational (e.g., Gauss elimination and matrix factorization) aspects will be studied.

This course is the first part of a two-semester sequence with MAT 314, with a focus on basic probability. It covers descriptive statistics, sample spaces and events, axioms of probability, counting techniques, conditional probability and independence, distribution of discrete and continuous random variables, joint distributions, and the central limit theorem.

This course is the second part of a two-semester course sequence with MAT 313, with a focus on applied statistics. It covers basic statistical concepts, graphical displays of data, sampling distribution models, hypothesis testing, and confidence intervals. A statistical software package is used.

Ordinary differential equations of first-order and first-degree, high order linear ordinary differential equations with constant coefficients, and properties of solutions.

A survey of Euclidean, non-Euclidean, and other geometries. The emphasis will be on formal axiomatic systems.

An axiomatic treatment of groups, rings, and fields that bridges the gap between concrete examples and abstraction of concepts to general cases.

This course will help students prepare for their future careers. Students may choose to either work in the classroom with a  mathematics instructor, for example as in-class tutors or teaching assistants, or work for an external organization under the supervision of a professional from the organization and a Gallaudet instructor. Students should consult with their academic advisors and the mathematics program internship coordinator to inquire about internship opportunities. Whether students work on or off-campus, their internship experience must consist of a minimum of 110 hours and be related to mathematics.  External internships must be approved by the mathematics program internship coordinator and meet Gallaudet Career Education and Professional Development Office requirements.

This course is the first part of a two-semester course sequence with MAT 456. This course covers a theoretical approach to calculus of functions of one and several variables. Limits, continuity, differentiability, Reimann integrability, sequences, series, and contour integration.

This course is for STM majors who are in their last year of the program. Students will produce two major products: (1) a grant proposal to a national or private agency and (2)interdisciplinary group project. In addition, students will discuss future career plans, examine contributions of different deaf scientists to science, and engage in discussions on science ethics and science literacy.

Elective mathematics courses 6 hours

Choose from the following:

A survey of the history of mathematics from antiquity through modern times.

A study of properties of integer numbers. Divisibility of integers, primes and greatest common divisors, congruencies, Euclidean algorithm, Euler Phi-function, quadratic reciprocity and integer solutions to basic equations, Diophantine equations, and applications to cryptography and primality testing.

This is an introductory course in cryptography. It covers classical cryptosystems, Shannon's perfect secrecy, block ciphers and the advanced encryption standard, RSA cryptosystem and factoring integers, public-key cryptography and discrete logarithms, and linear and differential cryptanalysis.

This course covers linear programming, the simplex algorithm, duality theory and sensitive analysis, network analysis, transportation, assignment, game theory, inventory theory, and queuing theory.

Numerical differentiation, integration, interpolation, approximation of data, approximation of functions, iterative methods of solving nonlinear equations, and numerical solutions of ordinary and partial differential equations.

This course covers statistical techniques with applications to the type of problems encountered in real-world situations. These topics include categorical data analysis, simple linear regression, multiple regression, and analysis of variance. A statistical software package is used.

This is an introductory course in complex analysis. The algebra of complex numbers, analytic functions, contour integration, Cauchy integral formula, theory of residues and poles, and Taylor and Laurent series.

This course is the second part of a two-semester course sequence with MAT 455. This course covers a theoretical approach to calculus of functions of one and several variables. Limits, continuity, differentiability, Reimann integrability, sequences, series, and contour integration.

Special topics in the discipline, designed primarily for seniors who are majors or minors. Students may enroll in 495 Special Topics multiple times, as long as the topics differ.

###### Program Outcomes

Demonstrate competence in discussing mathematical and statistical concepts in writing and in American Sign  Language.

Demonstrate an understanding of the analytical foundations of the core fields of Algebra, Calculus,  Geometry, and Statistics.

Demonstrate competence in the computational techniques of Calculus, Statistics, and Linear Algebra, including through the use of software.

Demonstrate an understanding of the fields of Mathematics and Statistics by exploring their applications, history, importance in reproducible and rigorous quantitative research, ethical decisions, and career opportunities.

Demonstrate an understanding of the importance of the collection, analysis, and interpretation of data and of evidence-based decision-making for questions of personal wellness choices, civic discourse within communities, and/or public policies.

## Job Outlook

B.A. in Mathematics

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