MATH009     COMPUTATIONAL SKILLS

3 sh

This is a one-term course in arithmetic or pre-algebra and is intended for students who need to improve their basic computational skills.  It contains work with whole numbers, fractions, decimals, ratio and proportion, percents, descriptive statistics, geometry and measures, signed numbers, and solving simple equations and problems.  This course does not count towards graduation.

MATH100     ESSENTIALS OF ALGEBRA

3 sh

This is a one-term introductory algebra course and is intended for students who have a firm background in arithmetic but need to improve their algebra skills in preparation for general education mathematics courses.  It covers real and rational numbers and algebraic expressions, solving equations and inequalities, polynomials, graphs, systems of equations, radicals, and quadratic equations.  MATH100 is restricted to students with appropriate placement test scores.  Ineligible students will not be allowed to register.

MATH101     TOPICS IN MATHEMATICS

3 sh

The mathematical content of the general education program.  The topics presented come from a variety of mathematical fields such as: number theory, topology, set theory, algebra, and analysis.  Each of the topics included in the course is subjected to careful mathematical analysis.  Prerequisite:  MATH100 or placement by the Department of Mathematics. Fulfills General Education Requirements.

MATH102     NUMBER SYSTEMS (previous title Mathematics for Elementary Teachers 1)

3 sh

Along with Geometry and Statistics (MATH215), the course provides the mathematical ideas and skills for teachers of grades K-6.  Topics included in Number Systems are problem solving, sets and relations, systems of numeration, number systems, and consumer mathematics.  Prerequisite:  MATH100 or Placement by the Department of Mathematics. Fulfills General Education Requirements.

MATH107     BASIC STATISTICS I

3 sh

The course presents both basic concepts and computational methods involved in the analysis of sample distributions, with consideration given to probability theory, and a thorough introduction to statistical inference.  Prerequisite:  MATH100 or Placement by the Department of Mathematics. Fulfills General Education Requirements.

MATH108     BASIC STATISTICS II

3 sh

The major topics are regression and analysis of variance.  Multiple regression, along with both one and two-way analysis of variance, are studies. Prerequisite:  MATH107.

MATH110     CONSUMER MATHEMATICS

3 sh

A practical course designed to provide the student with information and computational skills necessary for money management.  Topics include: interest, taxes, buying, credit, banking, insurance, annuities, international business, investments, and financial planning. Prerequisite:  MATH100 or Placement by the Department of Mathematics.  Fulfills General Education Requirements.

MATH112     INTERMEDIATE ALGEBRA

3 sh

Assists students in acquiring a thorough knowledge and proficiency in algebra.  It introduces the student to the rules for operating in algebraic expressions and the justification for these rules.  The contents of the course also include an introduction to the function concept, a thorough treatment of first and second-degree equations, topics in higher polynomial equations, and the algebraic structure of the number systems, such as the integers and rationales will also be explained.  MATH112 is not open to Mathematics and Mathematics Education majors except by permission of the chairperson.   Prerequisite:  MATH100 or placement by the Department of Mathematics.  Fulfills General Education Requirements.

MATH113     PRECALCULUS

3 sh

The major topics are: functions, polynomials, exponentials, logarithms, and trigonometric functions.  This material is treated in the modern spirit with emphasis placed on both the development of pertinent concepts as well as the acquisition of essential techniques.  The presentation of the topics is balanced between theory and application.  Although some treatment of the real numbers is included, the principal mathematical structure involved is the set of rational numbers and its subsets.  Prerequisite:  MATH112 or placement by the Department of Mathematics. Fulfills General Education Requirements.

1 sh

Designed to embed education program requirements into a required course and to support student achievement of Education Program requirements.  This course addresses topics taught in freshman seminars.  Restricted to first-year secondary education mathematics majors or B.A. mathematics majors.

3 sh

Concepts of functions and their graphs are defined and basic combinations of functions are introduced.  Properties and graphs of linear, quadratic, and periodic functions are discussed.  Trigonometric functions, identities and equations are discussed and graphs of various combinations of trigonometric functions are explored.  Some properties such as areas and volumes of geometrical figures are discussed and vectors are introduced.  Regression line and estimation of parameters are discussed.  Applications in Physical Sciences are also explored.  Restrictions upon student registration:  This course is designed for students who are required to take PHYS130 and PHYS131.  Prerequisite:  MATH112 or placement by the Department of Mathematics.  It may not be used as a prerequisite for MATH141.  Fulfills General Education Requirements.

MATH141     CALCULUS 1

3 sh

Algebraic functions, trigonometric functions, and elementary analytic geometry are reviewed.  Limits of functions and continuity are introduced.  The derivative of a function is defined and properties of the derivative are applied to a variety of problems.  The integral is defined and the Fundamental Theorem of Calculus is introduced and used in the evaluation of integrals.  Prerequisite: MATH113 or placement by the Department of Mathematics. Fulfills General Education Requirements.

MATH142     CALCULUS 2

3 sh

The calculus of transcendental functions is presented.  Integration is studied in depth, specifically techniques of integration and applications, as well as improper integrals.  Conic sections and indeterminate forms are studied.  Prerequisite:  MATH141. Fulfills General Education Requirements.

MATH180     MATHEMATICS FOR MANAGEMENT

3 sh

An introduction to the basic techniques for solving systems of linear equations and their extension to the simplex method for solving linear programming problems.  Conditional probability is re-examined and extended to Markov Processes.  If time permits, differentiation and integration from calculus will be introduced and employed to examine extreme value problems.  Prerequisite:  MATH107 and 112 or placement by the Department of Mathematics.  Fulfills General Education Requirements.

MATH205     FOUNDATIONS OF MATHEMATICS

3 sh

Provides the foundation that is necessary for students to make the transition to advanced mathematics.   Basic topics of Mathematical Logic with deductive reasoning as applied to mathematical proofs are studied in detail.  Mathematical Induction, Set Theory and Theory of Relations and Functions are studied with appropriate proofs.  Prerequisite:  MATH141.  Fulfills General Education Requirements.

MATH211     LINEAR METHODS

3 sh

Vector spaces, matrices, linear transformations, and systems of linear equations are defined and the properties of these structures are developed through examples and, to a lesser degree, proof-theoretic techniques.  Inner product spaces, eigenvalues, and eigenvectors are also explored.  Euclidean vector spaces are emphasized throughout.  Prerequisite:  MATH141.  Fulfills General Education Requirements.

MATH215     Statistics and Geometry (previous title Mathematics for Elementary Teachers  2)

3 sh

Along with Number Systems(MATH102), this course provides the mathematical ideas and skills for teachers of grades K-6.  Topics included are probability and statistics, geometry and measurement, functions, and analytic geometry.  Problem solving is emphasized throughout the course.  Prerequistie:  MATH100 or placement by the Department of Mathematics.  Fulfills General Education Requirements.

MATH225      HISTORY OF MATHEMATICS

3 sh

Provides a chronological development of the history of mathematics, interwoven with biographical sketches and outstanding achievement.  Begins with the great civilizations of antiquity and progresses through the first few decades of the twentieth century.  Addresses contributions from underrepresented groups in a variety of ways.  Students study how contributions from culturally diverse populations have significantly aided the development of the field of mathematics, and how mathematics has changed the culture of diverse populations. Prerequisite:  MATH141.  Fulfills General Education Requirements.

MATH243     CALCULUS 3

3 sh

Multivariate calculus and its applications are studied, along with three-dimensional analytic geometry.  A study of series, culminating with power series representation for functions, is presented.  Polar equations and their graphs are studied.  Prerequisite:  MATH142.  Fulfills General Education Requirements.

MATH244     CALCULUS 4

3 sh

Concludes the undergraduate study of calculus with a detailed treatment of vector analysis, culminating in the three integral theorems of vector analysis:  the divergence theorem, Green's theorem, and Stokes' theorem.  Prerequisite:  MATH243.  Fulfills General Education Requirements.

MATH301     DIFFERENTIAL EQUATIONS

3 sh

The techniques for solving linear, nonlinear, homogeneous, and nonhomogeneous ordinary differential equations along their applications including initial-value and boundary-value problems.  Prerequisite:  MATH243.  Fulfills General Education Requirements.

MATH302     NUMBER THEORY

3 sh

Study of the divisibility properties of the integers.  Topics include the congruence relations, arithmetic functions, Gauss' Law of Quadratic Reciprocity, and Diophantine equations as well as applications such as cryptography.  Prerequisite:  MATH205.  Fulfills General Education Requirements.

MATH307     FOUNDATIONS OF GEOMETRY

3 sh

The course is an axiomatic study of elementary geometries including finite geometry, absolute (neutral) geometry, Euclidean geometry, Lobachevskian geometry, and Riemannian geometry.  Historical and cultural frameworks for these geometries are provided.  Prerequisite:  MATH205.  Fulfills General Education Requirements.

MATH310     MODERN ALGEBRA I

3 sh

Investigates algebraic structures including groups, rings, and fields.  Special emphasis is placed on the concept of isomorphism as well as applications to the algebra of the secondary educational classroom.  Prerequisite:  MATH205. Fulfills General Education Requirements.

MATH311     ELEMENTS OF LINEAR ALGEBRA

3 sh

Systems of linear equations, determinant function, vector spaces, inner product spaces, linear transformations, eigenvalues, and eigenvectors  are defined and properties of these structures are developed through proof-theoretic techniques.  Applications to areas such as geometry, economics, physical science, social science are explored.  Prerequisite:  MATH205.  Fulfills General Education Requirements.

MATH312     PROBABILITY AND STATISTICS

3 sh

A study of the mathematization of probability situations;  the application of analysis and set theory to the models involved, and the statistics and statistical inference, which results.  Both computational and functional approaches to probability are examined.  Prerequisite:  MATH243.  Fulfills General Education Requirements.

MATH320     LINEAR PROGRAMMING

3 sh

The theory of linear programming as well as applications in which linear programming finds its utility, including operations research/management science, game theory, and graph theory.  Prerequisite:  MATH211.  Fulfills General Education Requirements.

MATH328     MATHEMATICAL SCIENCES SEMINAR

3 sh

This seminar has featured such topics as the study of the history of mathematics, the impact and potential effects of computers upon society, and the study of mathematics as it occurs with society in the forms of puzzles, games, and other types of recreation. 

MATH350     NUMERICAL METHODS

3 sh

An introduction to numerical methods in the solution of non-linear equations, systems of linear equations, numerical integration, and numerical differentiation.  The course will entail both mathematical rigor and computational aspects of some widely used numerical methods.  Commercially produced programs from the IMSL library will be used. Prerequisite:  MATH243. Fulfills General Education Requirements.

3 sh

Provides an advanced treatment of mathematical content typically associated with the secondary mathematics curriculum.  The strategies of concept analysis, problem analysis, and mathematical connections are used to investigate secondary mathematics.  Prerequisites:  Open to any senior secondary mathematics education student or by permission of instructor.  MATH141, 142, 243, 205,, 302, 307, 310, and 311.

MATH401     REAL ANALYSIS I

3 sh

Provides a mathematically rigorous introduction to analysis of a real valued function of a single real variable.  Mathematical logic, set theory, relevant topological and algebraic properties together with proof techniques are heavily utilized throughout the course.  Convergence, Continuity, Differentiation, Integration and their interconnections are studied with mathematical integrity.  Prerequisites:  MATH205 and 243.  Fulfills General Education Requirements.

MATH402     REAL ANALYSIS II

3 sh

A continuation of MATH401 - Real Analysis I.  Convergence questions regarding sequences and series of real functions are investigated.  The Lebesque integral is defined and its existence and properties are investigated.  Several basis theorems about Fourier series are explained and proved.  Real-valued functions of several real variables are defined and several related theorems are deduced.  Prerequisite:  MATH401.  Fulfills General Education Requirements.

MATH404     APPLIED MATHEMATICS

3 sh

The investigation of the concept of mathematical model as it is used in Applied Mathematics.  Different models are presented as a means of providing solutions to practical problems.  Prerequisite:  MATH301.  Fulfills General Education Requirements.

MATH410     INTRODUCTION TO TOPOLOGY

3 sh

The course is an introduction to the elements of set theory and topology.  Topics could include introductory set theory, a detailed study of the real line, topological spaces, metric spaces, functions and continuity, compactness, connectedness, completeness, product spaces, function spaces.  Prerequisite:  MATH401.  Fulfills General Education Requirements.

Provides the first in a two-course sequence of methods of teaching mathematics in grades 7-12.  This course includes field experiences and practice teaching.  The concentration in this course is on the nature of mathematics, psychology of learning mathematics, teaching of mathematics, history of mathematics education, national and state standards, lesson planning, technology, and diversity issues.  In addition to these, as the specific topics arise, the course helps students more deeply understand the mathematics concepts they will be teaching.  Restrictions upon registration:  Course is open to any secondary mathematics education student with the prerequisites of MATH141, EDTF101, and PSYC103.  Students should also be enrolled in at least MATH142 and MATH205 during the same semester as this course.

Provides the second in a two-course sequence of methods of teaching mathematics in grades 7-12.  This course includes field experiences and practice teaching.  The concentration in this course is on instructional strategies for specific content, the problems of practice, curriculum, unit and lesson planning, assessment, reading and writing strategies in mathematics, technology, diversity issues, adaptations for special needs, and professionalism.  In addition to these, as the specific topics arise, the course helps students more deeply understand the mathematics concepts they will be teaching.  Restrictions upon registration:  Course is open to any secondary mathematics education student who has achieved candidacy, is eligible to student teach within the next two semesters, and has completed and presented the developing portfolio.

7/7 sh

Student teaching provides the capstone experience for preservice teachers.  Two student teaching experiences are provided at two levels (appropriate to certification areas and grade level ranges).  Supervised practice in classrooms with certified teachers introduces the student to all aspects of the teaching day.  University professors supervise the student teachers and conduct weekly practicum sessions.  Restrictions:  To register, a student must meet Pennsylvania State Teacher Education Guidelines in overall average and average in major, no courses less than a “C” in professional courses and a successful clinical field experience.

6 sh

Provides the first of two capstone experiences (one at each level appropriate to certification areas and grade level ranges) for pre-service teachers through a student teaching experience required for certification in secondary mathematics.  Supervised practice in classrooms with certified teachers and regular practicum sessions, according to prescribed guidelines, introduce the student to the range and scope of a professional educator's responsibilities.  Restrictions:  To register, a student must meet Pennsylvania State Teacher Education Guidelines in overall average and average in major, no courses less than a “C” in professional courses and all requirements of early field experiences.