# 300

## 13-300 Differential Equations

This course focuses on ordinary differential equations. It includes variable separable equations, equations with homogeneous coefficients, exact equations, first order linear equations, applications, homogeneous linear equations with constant coefficients, undetermined coefficients, variation of parameters, power series solutions, linear systems of equations and Laplace transforms.

3

13-250.

## 13-305 Linear Algebra

The study of matrices and matrix algebra, systems of linear equations, matrix inverse and elementary matrices, properties of determinants, vector spaces, especially Rn vectors, linear independence, basis sets, inner products and orthogonality.

3

### Prerequisites

13-201.

This course begins with the Gram-Schmidt process. Other topics of study are Eigenvalues and Eigenvectors, change of basis, linear transformations, diagonalization, symmetrical and similar matrices. Applications of these concepts include quadratic forms and linear programming.
3

13-305.

## 13-310 Discrete Mathematics

An introduction to discrete structures, this course covers such topics as sets, functions, relations, basic logic, proof techniques, the basics of counting and probability, algorithms, graphs and trees.

4

### Prerequisites

13-120 or successful completion of three years of high school Mathematics including Trigonometry.

## 13-311 Mathematical Techniques for the Sciences

This course prepares science students to organize, analyze, visualize, and interpret their data using mathematical techniques. Students learn to use a variety of computer applications to model systems and process measurement data specific to their discipline. They also learn the mathematics that powers these applications.

4

### Prerequisites

13-200 and 13-201, or 13-211; Senior standing in Biology, Chemistry, Mathematics, Computer Science, or Physics.

## 13-315 Probability and Statistics I

The course covers the basic principles of probability and statistics, with applications. Topics include descriptive statistics, the axioms of probability, counting techniques, conditional probability, independence, discrete and continuous random variables, expected value, variation, normal, binomial and Poisson distributions, probability density functions, joint distributions, and point estimation.

3

13-201.

### Corequisites

Pre or co-requisite 13-325

## 13-316 Probability and Statistics II

A continuation of 13-315. This course covers confidence intervals for mean, proportion, and standard deviation, hypothesis testing, inferences based on two samples, analysis of paired data, analysis of variance, and linear regression and correlation
3

13-315.

## 13-320 Theories of Geometry

The study of Euclid’s geometry, its strengths and weaknesses, famous and advanced theorems and its impact on the development of geometry. This latter includes axiomatic systems and proofs, the parallel axiom and the analysis of constructions and transformation geometry.

3

13-201.

## 13-325 Foundations of Advanced Mathematics

This course provides a gateway into the more abstract and theoretical expectations of upper-level mathematics courses. The course includes a brief introduction of set theory, symbolic logic, complex numbers, and relations especially as they apply to proof. The course also introduces methods of mathematical proof such as direct proof, indirect proof, proof by contradiction, and proof by induction.
2

### Prerequisites

Prior or concurrent enrollment in 13-201.

## 13-327 Introduction to Number Theory

Number theory is the study of the integers. Topics include divisibility, primes, congruences, number theoretic functions, quadratic residues, and primitive roots, with additional topics selected from among Diophantine equations, Pythagorean triples, Fermat's Last Theorem, sums of squares, continued fractions, cryptography, primality testing, and Pell's equation.
3

13-200.

## 13-330 History of Mathematics I

The history of Mathematics from the Babylonian period to the early 17th century. The mathematical emphasis is on famous theorems of each era. Biographical information on mathematicians and historical analysis of each era are included.

3

13-201.

## 13-331 History of Mathematics II

The history of mathematics beginning with the 17th century to modern time. The mathematical emphasis is on famous theorems of each era. Biographical information on mathematicians and historical analysis of each era are included.
3

13-201.

## 13-350 Numerical Analysis

Students examine floating point arithmetic, polynomial interpolation, numerical methods of integration, numerical solution of non-linear equations and numerical linear algebra.

3

### Prerequisites

13-325 and 70-200.

## 13-360 Real Analysis I

This course provides a formal presentation of the real number system and Euclidean vector spaces (inner products, norms and distance functions), compactness and connectedness, continuity, differentiation, and integration.

3

### Prerequisites

13-250 and 13-325.

## 13-361 Real Analysis II

A continuation of 13-360, this course studies uniform convergence, sequences and series of functions, differential and integral calculus for functions of several variables, the Implicit Function Theorem and the Inverse Function Theorem.

3

13-360.