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Department of Mathematics |
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| 323 Anderson Hall (610)436-2440 info@math.wcupa.edu | |
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MAT 000 Fundamentals of Algebra (3)
(offerings:
current,
next semester
)
A preparatory course to remediate basic algebraic skills. Students scoring between 440-480 on the mathematics section of the Scholastic Aptitude Test (SAT) and who do not pass the mathematics test during their orientation program are placed in this course prior to any other mathematics course. Credits earned in 000-level courses do not count towards the 128 hours of credit needed for graduation. The course must be passed with a grade of C- or better, or be repeated.
MAT 001 Fundamental Skills in Arithmetic (3)
(offerings:
current,
next semester
)
A course designed to remediate basic arithmetic skills and to introduce elementary algebra. In general, students placed in MAT 001 have scored below 440 on the math SAT and have not taken high school algebra. Students are being prepared to take Fundamentals of Algebra (MAT 000) and must earn at least a C- to enroll in that course. A student in MAT 001 does not earn credit toward graduation for this course. Elementary and special education majors in need of algebraic and/or arithmetic remediation must enroll in MAT 001.
MAT 101 Mathematics for Elementary Teachers I (3)
(offerings:
current,
next semester
)
Sets; functions; logic; development of whole numbers, integers, and rationals (including ratios, proportions, and percents); number theory; problem solving. For early childhood, elementary education, and special education majors only.
MAT 102 Mathematics for Elementary Teachers II (3)
(offerings:
current,
next semester
)
Development of real numbers; geometry; measurement; probability and statistics; problem solving. For elementary education and special education majors only. PREREQ: MAT 101.
MAT 103 Introduction to Mathematics (3)
(offerings:
current,
next semester
)
This course is a liberal arts introduction to the nature of mathematics. Topics are chosen from among logic, graph theory, number theory, symmetry (group theory), probability, statistics, infinite sets, geometry, game theory, and linear programming. These topics are independent of each other and have as prerequisite the ability to read, reason, and follow a logical argument.
MAT 105 College Algebra and Trigonometry (3)
(offerings:
current,
next semester
)
A unified course in algebra and trigonometry. PREREQ: High school algebra.
MAT 107 College Algebra (3)
(offerings:
current,
next semester
)
A thorough treatment of college algebra. Topics covered include the study of polynomial, exponential, and logarithmic functions, plus systems of linear equations. PREREQ: SAT score of 450 (original scale), 480 (recentered scale) or above, or passing a placement test, or obtaining at least a C- in MAT 000.
MAT 108 Brief Calculus (3)
(offerings:
current,
next semester
)
An intuitive approach to the calculus of one and several variables with emphasis on conceptual understanding and practical application. PREREQ: MAT 107.
MAT 110 Precalculus (3)
(offerings:
current,
next semester
)
A preparation for MAT 161, Calculus I. Topics include polynomial and rational functions, algebra of functions, graphs of functions, transcendental functions, trigonometry, series, induction, and complex numbers.
MAT 121 Statistics I (3)
(offerings:
current,
next semester
)
Basic concepts of statistics. Frequency distributions, measures of central tendency and variability, probability and theoretical distribution, significance of differences, and hypothesis testing. For nonmathematics majors.
MTL 121 Statistics Lab I (1)
(offerings:
current,
next semester
)
Introduces the student to using and programming the computer to solve statistical problems and to aid the student in understanding statistical concepts.
MAT 122 Statistics II (3)
(offerings:
current,
next semester
)
Continuation of MAT 121. Inference about the means, standard deviations and proportions, goodness of fit, analysis of variance, regression analysis, correlation, and nonparametric tests. PREREQ: MAT 121.
MAT 151 Introduction to Discrete Mathematics (3)
(offerings:
current,
next semester
)
Set theory, Boolean logic, elementary combinatorics, proofs, simple graph theory, and simple probability.
MAT 161 Calculus I (4)
(offerings:
current,
next semester
)
Differential and integral calculus of real-valued functions of a single real variable, with applications. PREREQ: Good working knowledge of high school algebra and trigonometry demonstrated by a math SAT score of 650 or above, or a C- or above in MAT 105 or MAT 110.
MAT 162 Calculus II (4)
(offerings:
current,
next semester
)
Continuation of MAT 161 including the study of series, methods of integration, transcendental functions, and applications to the sciences. PREREQ: MAT 161.
MAT 209 Topics in Mathematics for the Elementary Teacher (3)
(offerings:
current,
next semester
)
Introduction to programming in BASIC; computer uses for the classroom teacher; descriptive statistics with applications for teaching; and measurements of length, area, volume, and temperature that focus on the SI metric system with practice in the classroom. Additional topics in applied mathematics will be considered. PREREQ: MAT 102.
MAT 211 Linear Algebra (3)
(offerings:
current,
next semester
)
An introduction to linear algebra. Topics covered include matrices, systems of linear equations, vector spaces, linear transformation, determinants, eigenvalues, spectral theorem, and triangulation.
MAT 212 Algebra for Elementary Teachers (3)
(offerings:
current,
next semester
)
Formal structure of groups, rings, and fields with examples from the elementary curriculum. Topics from linear algebra including matrices, determinants, and linear programming. PREREQ: MAT 102.
MAT 221 Applied Statistics (3)
(offerings:
current,
next semester
)
Probabilities, discrete and continuous probability distributions, methods of estimation, and hypothesis testing. PREREQ: CSC 141 (or equivalent) and MAT 162 (or equivalent).
MAT 231 Foundations of Geometry (3) (offerings:
current,
next semester
)
Geometric foundations from an advanced viewpoint. Topics are chosen from euclidean and noneuclidean geometrics. Offered in the spring semester.
MAT 232 Differential Geometry (3) (offerings:
current,
next semester
)
Classical differential geometry from a modern viewpoint. Curves and surfaces and shape operators. Introduction to Riemann geometry. PREREQ: MAT 262.
MAT 233 Geometry for Elementary Teachers (3)
(offerings:
current,
next semester
)
Modern informal approach to two- and three-dimensional geometric figures, measurement, similarity, congruence, coordinate geometry, and the postulational method. PREREQ: MAT 102.
MAT 261 Calculus III (3)
(offerings:
current,
next semester
)
The calculus of several variables. Topics include polar coordinates, vectors and three-dimensional analytic geometry, differentiation of functions of several variables, multiple integrals, and line and surface integrals. PREREQ: MAT 161 and MAT 162.
MAT 262 Calculus IV (3)
(offerings:
current,
next semester
)
The calculus of vector-valued functions of a vector variable. Derivatives and properties of the derivative including the chain rule, fields and conservative fields, integration, and Green's, Stokes', and Gauss' theorems. PREREQ: MAT 261.
MAT 281 Discrete Mathematics (4)
(offerings:
current,
next semester
)
This course is designed to provide a foundation for the mathematics used in the theory and application of computer science. Topics include mathematical reasoning, the notion of proof, logic, sets, relations and functions, counting techniques, algorithmic analysis, modelling, cardinality, recursions and induction, graphs, and algebra. PREREQ: MAT 162.
MAT 321 Combinatorics and Graph Theory (3)
(offerings:
current,
next semester
)
Introduction to set theory, graph theory, and combinatorial analysis. Includes relations, cardinality, elementary combinatorics, principles of inclusion and exclusion, recurrence relations, zero-one matrices, partitions, and Polya's Theorem. PREREQ: CSC 101 or 141, and MAT 262 or MAT 281.
MAT 343 Differential Equations (3)
(offerings:
current,
next semester
)
The general theory of nth order, and linear differential equations including existence and uniqueness criteria and linearity of the solution space. General solution techniques for variable coefficient equations, series solutions for variable coefficient equations, and study of systems of linear equations. PREREQ: MAT 261. Offered in the spring semester.
MAT 349 Teaching Mathematics in Early Childhood (3)
(offerings:
current,
next semester
)
Concepts, learning aids, syllabi, texts, and methods in early childhood mathematical teaching. PREREQ: MAT 101.
MAT 350 Foundations of Mathematics Education (3)
(offerings:
current,
next semester
)
Historical overview of mathematics education with emphasis on influential curricular programs, implications of learning theory, significance of research, identification of current issues, organizational alternatives for the classroom, and evaluation resources. PREREQ: MAT 261. Offered in the fall semester.
MAT 351 Teaching Mathematics in Elementary Schools I (3)
(offerings:
current,
next semester
)
Concepts, learning aids, syllabi, texts, and methods in elementary school mathematics. PREREQ: MAT 101-102.
MAT 352 Teaching Mathematics in Elementary Schools II (3)
(offerings:
current,
next semester
)
Techniques for teaching children concepts such as geometry in two and three dimensions, number sentences, graphing, ratios and percentages, quantifiers, etc. Use of laboratory materials will be emphasized. PREREQ: MAT 351. Offered in the spring semester.
MAT 354 Techniques of Teaching Secondary School Mathematics (3)
(offerings:
current,
next semester
)
Techniques used in the presentation of specific mathematical concepts, associated materials, levels of questioning, and motivational devices. Scope and sequence of secondary mathematics topics. Criteria for text evaluation. Preview of student teaching. PREREQ: MAT MAT 350. Offered in the spring semester.
MAT 357 Teaching Mathematics to the Handicapped (3)
(offerings:
current,
next semester
)
Methods and materials associated with the presentation of mathematics to the handicapped. Emphasis on individualization and involving thinking skills at the concrete level. Evaluative and interpretive techniques are included. PREREQ: MAT 101-102.
MAT 390 Seminar in Mathematics Education (3)
(offerings:
current,
next semester
)
Typical topics are remedial programs, low achiever programs, materials for mathematics education, methodology in mathematics education, mathematics and the computer, theories of mathematics education, and analysis of research in mathematics education. PREREQ: MAT 351.
MAT 400 History of Mathematics for Elementary Teachers (3)
(offerings:
current,
next semester
)
History and development of elementary mathematics from primitive times to the discovery of calculus. Problems of the period are considered. PREREQ: MAT 212 and MAT 233.
MAT 401 History of Mathematics (3) (offerings:
current,
next semester
)
Development of mathematics from the Babylonian era to the 18th century. Some modern topics included. PREREQ: MAT 261.
MAT 405 Special Topics in Mathematics (3)
(offerings:
current,
next semester
)
Topics announced at the time of offering.
MAT 411-412 Algebra I-II (3) (3)
(offerings:
current,
next semester
)
Abstract algebra. Algebraic systems, groups, rings, integral domains, and fields. PREREQ: MAT 261. MAT 411 must precede 412.
MAT 414 Theory of Numbers (3)
(offerings:
current,
next semester
)
Properties of integers; primes, factorization, congruences, and quadratic reciprocity. PREREQ: MAT 262.
MAT 421-422 Mathematical Statistics I-II (3) (3)
(offerings:
current,
next semester
)
Probability theory, discrete and continuous random variables, distributions, and moment generating functions. Statistical sampling theory, joint and interval estimation, test of hypothesis, regression, and correlation. PREREQ: MAT 262. MAT 421 must precede 422.
MAT 425 Numerical Analysis (3)
(offerings:
current,
next semester
)
Numerical methods for the approximate solution of applied problems. Interpolation theory, curve fitting, approximate integration, and numerical solution of differential equations. PREREQ: CSC 115 or 141, and MAT 262.
MAT 427 Introduction to Optimization Techniques (3)
(offerings:
current,
next semester
)
Nature of optimization problems: deterministic and stochastic, and discrete and continuous. Computer methods of solution, systematic and random search, linear quadratic, dynamic programming, and others. PREREQ: CSC 115 or 141, and MAT 262.
MAT 432 Topology (3)
(offerings:
current,
next semester
)
Elements of point set topology. Separation axioms. Connectedness, compactness, and metrizability. PREREQ: MAT 262.
MAT 441-442 Advanced Calculus I-II (3) (3)
(offerings:
current,
next semester
)
A rigorous treatment of the calculus of a single real variable. Topics in several real variables and an introduction to Lebesque integration. PREREQ: MAT 262. MAT 441 must precede 442.
MAT 443-444 Applied Analysis I-II (3) (3)
(offerings:
current,
next semester
)
The techniques of analysis applied to problems in the physical sciences. Topics include partial differential equations, orthogonal functions, complex integration, and conformal mapping. PREREQ: MAT 262. MAT 443 must precede 444.
MAT 445 Complex Variables (3)
(offerings:
current,
next semester
)
Introduction to functions of a complex variable. Analytic functions, mappings, differentiation and integration, power series, and conformal mappings. PREREQ: MAT 262.
MAT 490 Seminar in Mathematics (3)
(offerings:
current,
next semester
)
Topics in mathematics selected for their significance and student-instructor interest. Independent study and student reports, oral and written. PREREQ: Senior standing and consent of department chairperson.
MAT 493 Mathematical Modeling (3)
(offerings:
current,
next semester
)
The idea of a mathematical model of a real situation. Techniques and rationales of model building. Examples from the life, physical, and social sciences. PREREQ: MAT 262 and MAT 343.
This course may be taken again for credit.
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