Courses of Mathematics at Albright College
COURSES
MAT 100
Pre-Calculus Mathematics
A review of algebra and trigonometry intended to be taken before 107 or 105 by those students whose background in algebra and trigonometry is insufficient. The major emphasis is on the function concept. Elementary analytic geometry is discussed, along with algebra, composition of functions, inverse functions, trigonometry, and logarithmic and exponential functions.
MAT 103
Discrete Mathematics I
An introduction to the theory and application of discrete mathematics. Topics include logic, sets, functions and relations, combinations and elementary probability.
MAT 104
Discrete Mathematics II
A continuation of MAT 103, this course includes trees and graphs, recurrence relations, elementary group theory and selected topics in computer science.
MAT 105
Discrete Mathematics and Calculus with Business/Economics Applications
Designed as a one-semester course for concentrators in business administration or economics, topics such as linear functions and models; matrices and matrix algebra; linear systems; functions and graphs; derivatives and integrals; and extremization are included. Partial differentiation also is introduced.
MAT 107
Calculus and Analytic Geometry I
Fundamental concepts of functions of one variable. Topics include: limits, continuity differentiation, derivative applications, curve sketching, related rates and maxima-minima problems. Introduction to indefinite and definite integration including the fundamental theorems, and numeric approximation techniques are also covered. This is normally the first mathematics course taken by students entering a math or math-related curriculum.
MAT 108
Calculus and Analytic Geometry II
A continuation of MAT 107. Applications of definite integration including volume, surface area, are length and work. Also included is the study of transcendental functions and integration techniques, indeterminate forms and improper integrals.
Prerequisite: MAT 107
MAT 110
Elementary Statistics
This course gives students a general overview of modern statistics. Topics include: organization of data; probability and probability distributions; measures of central tendency and variability; normal distributions; sampling; hypothesis testing; correlation and regression. A TI-89 graphing calculator is highly recommended.
MAT 207
Calculus III
A continuation of MAT 108. Topics include sequences and infinite series, polar coordinates, parametric representation, vectors, analysis of functions of two (or more) variables, multiple integration and line integrals. Normally taken by mathematics concentrators in the first semester of the sophomore year.
Prerequisite: MAT 108
MAT 302
Differential Equations
A study of solution techniques for ordinary differential equations. Topics include the principal types of equations of first and second order, linear equations with constant coefficient, higher order linear and non-linear equations, series solutions, operational methods, systems of equations and modeling problems. Runge- Kutta and other numerical approximation methods are also covered.
Prerequisite: MAT 207, 307
MAT 304
Functions of a Complex Variable
An introduction to the theory of functions of complex variables: derivatives and integrals; Cauchy’s theorem; power series; theory of residues; and conformal mappings.
Prerequisite: MAT 207, 311
MAT 307
Linear Algebra
An introduction to matrix algebra; linear equations; linear dependence; determinants; vector spaces; linear transformations; and eigen problems.
Prerequisites: MAT 108 and 311 or permission of the department
MAT 308
Modern Algebra
An introduction to groups with topics selected from number theory, rings, fields, ideals and polynomial rings.
Prerequisite: MAT 311 or permission of the department
MAT 311
Foundation of Mathematics
An introduction to abstract mathematics. Topics include symbolic logic, methods of proof (direct, contradiction and induction), set theory, relations, functions, countable and uncountable sets. Normally taken by mathematics concentrators in the first semester of the sophomore year.
Prerequisite: MAT 108 or permission of the department
MAT 312
Introduction to Topology
Definitions and properties of topological spaces, metric spaces, continuity, homeomorphisms, separation axioms, compactness and connectedness. Prerequisites: MAT 207, 311 or permission of the department
MAT 315
Partial Differential Equations
Orthogonal functions; Sturm-Liouville system; initial and boundary value problems; Fourier series; higher transcendental functions; separation-of-variables method; and other methods of solution of equations of mathematical physics.
Prerequisite: MAT 207, 302
MAT 316
Mathematical Statistics
An introduction to mathematical statistics at the level presupposing a knowledge of calculus. Descriptive and inferential statistics are included. Hypothesis testing, estimation, analysis of variance and nonparametric methods are discussed.
Prerequisite: MAT 207 or 108 with departmental approval
MAT 317
Numerical Methods
A study of numerical methods involved in interpolation; differentiation and integration; solution of equations and systems of equations; solution of differential equations; and fitting of empirical data, with emphasis in those procedures that can be most readily programmed into a calculator or computer. Applications are made to the sciences and engineering. Computer programming knowledge is assumed.
Prerequisite: MAT 207
MAT 318
Geometry
This course is intended primarily for those students planning to enter the field of secondary education. It begins with a study of the most important ideas of Euclidean plane geometry, but also considers the historical significance of Euclid’s original postulates. Special attention is given to the notion of parallelism of lines and the resulting non-Eu clidean geometries when the axiom of parallelism is altered. Differential geometry also is introduced as a means of studying curves, surfaces and curves on surfaces.
Prerequisites: MAT 207 and 311
MAT 321
Advanced Calculus I
Designed to take a rigorous look at definitions, theorems and concepts taken from the foundational calculus courses. Rigorous treatment given to topics such as continuity, mean-value theorems, analysis of functions of several variables, extremization and limits. Other topics include sequences, series and the Heine-Borel covering theorem.
Prerequisites: MAT 207, 311
MAT 340
Topics
Designed to cover topics of interest that are not covered in other courses.
MAT 491
Seminar I (W)
A seminar in topics selected by the course instructor in which independent learning is stressed. The student is expected to present both oral and written reports on topics covered in the seminar.
Prerequisite: Senior standing or permission of the department
MAT 492
Seminar II (W)
A seminar in which each student selects a topic with the approval of the course instructor. The student is expected to present both oral and written reports. This seminar is to be taken in the final semester of the student’s course work. Exceptions require the approval of the department. Prerequisite: Senior standing or permission of the department
Tags: calculus and analytic geometry, composition of functions, definite integration, economics topics, elementary group, elementary probability, functions and graphs, fundamental theorems, geometry ii, indeterminate forms, matrix algebra, maxima minima problems, prerequisite mat, recurrence relations