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- The student attains a firm foundation of fundamental mathematical concepts, methods and language sufficient to support further academic work or a career in areas requiring mathematical understanding.
- The student attains knowledge and skills to undertake independent learning beyond formal study.
- The student applies mathematical skills and knowledge to solve problems and analyze new situations in mathematics and related areas.
- The student communicates mathematical ideas, both orally and in writing, with clarity and precision.
Requirements for the Major in Mathematics. Students complete the equivalent of 55 semester hours as described.
|Semester Hours||View Full Course Catalog >>|
|4 MATH-112 Calculus II|
|4 MATH-180 Statistical Methods|
|4 MATH-201 Linear Algebra|
|4 MATH-211 Multivariate Calculus|
|4 MATH-221 Discrete Structures|
|2 MATH-231 Foundations of Analysis|
|4 MATH-321 Abstract Algebra|
|4 MATH-353 Differential Equations|
4 One 300-level or above mathematics course
8 Two 400-level mathematics courses
|1-4 MATH-500 Senior Colloquium|
|4 CSCI-181 Principles of Computer Science|
8 CSCI-281 Data Structures plus another 150-level or above computer science or information systems course, or Inductory Physics I (PHYS-202, PHYS-203 and PHYS-204) and Introductory Physics II (PHYS-205 or PHYS-206) or DATA-301 Data Mining and DATA-401 Machine Learning
Minor in Mathematics. The minor completes 24 semester hours of mathematics courses above the 108 level with grades of C- or better. Requirements include MATH-112 Calculus II, MATH-201 Linear Algebra and MATH-221 Discrete Structures, with at least four semester hours at the 300 level or above.
MATH-099 College Mathematics Preparation
Topics may include sets, radicals, polynomials, factoring, inequalities, linear and quadratic equations, functions, exponents, and simple descriptive statistics. Intended for students not ready for college credit math; placement in this course is determined by the Department of Mathematics. Grade is S/U. 0 SH.
MATH-101 Precalculus Mathematics
Topics include algebra, functions, graphing, exponents, logarithms, exponential functions, trigonometry and solving word problems. Prerequisite: Based on placement results, some students may require a mathematics review course. 4 SH.
MATH-105 Introductory Topics
This is a two-semester-hour course meant to help education majors satisfy the Pennsylvania state requirement for six credits of college mathematics. Each course will cover a topic of the instructor's choice at an introductory level. Topics so far have included symmetry, counting, and math and music. This course does not count toward a math major or minor, and particular topics may overlap enough with other math courses to bar a student from taking both. Education majors will be given priority. Prerequisites: Usually none. 2 SH.
MATH-108 Introduction to Statistics
A basic introduction to data analysis, descriptive statistics, probability, Bayes' Theorem, distributions of random variables and topics in statistical inference. (Students may earn credit for only one of the introductory statistics courses offered by the departments of management, psychology or mathematics.) 4 SH. CC: Analytical Thought.
MATH-109 Statistics for Social Sciences
This course covers basic descriptive and inferential statistical techniques used in analyzing social science research data. The student becomes familiar with ways to organize and analyze data, communicate research results, translate statistical jargon into meaningful English, and understand basic theories underlying statistics, e.g., elementary probability theory. 4 SH. CC: Analytical Thought.
MATH-111 Calculus I
Differentiation and integration of polynomials, exponentials, logarithms and trigonometric functions rules of differentiation and applications. 4 SH. CC: Analytical Thought.
MATH-112 Calculus II
Techniques of integration, area, volume and arc length. Also includes improper integrals, L'Hopital's rule and power series. Prerequisite: MATH-111 Calculus I or equivalent. 4 SH. CC: Analytical Thought.
MATH-180 Statistical Methods
This course provides a broad overview of introductory statistical methods and data analysis. Topics include descriptive statistics, probability, probability distributions, statistical inferences on population means and population variances, multiple comparisons, categorical data, data analysis using linear regression and multiple regression, design of experiments, and analysis of variance. 4 SH. CC: Analytical Thought.
MATH-201 Linear Algebra
An elementary introduction to linear algebra. Topics include vectors, matrices, determinants, systems of linear equations, linear transformations, eigenvalues and eigenvectors. Also covers applications to computer graphics. Placement at MATH-111 Calculus I level or higher is strongly recommended. 4 SH. CC: Analytical Thought.
MATH-203 Math and Music
An exploration of the interplay of mathematics and music. Topics such as the Fourier theory of sound, consonance and dissonance scales, temperament, digital signal processing, sound synthesis, twelve tone music theory, and algorithmic composition will be covered in the course. Prerequisites: Sophomore standing and MATH-112 Calculus II. Some knowledge of music theory and computer programming would be helpful but is not required. 4 SH. CC: Interdisciplinary.
MATH-211 Multivariate Calculus
Calculus of several variables, partial derivatives, critical points, multiple integrals, gradient, curl, divergence, Green's Theorem and Stokes' Theorem. Prerequisites: MATH-112 Calculus II and MATH-201 Linear Algebra. 4 SH.
MATH-221 Discrete Structures
An elementary approach to fundamental algebraic concepts. Emphasizes logic, proof techniques, relations, functions, graphs, Boolean algebra and computer logic. Also stresses modular arithmetic, algebraic structures, counting principles, coding theory and finite state machines. Prerequisite: MATH-111 Calculus I. 4 SH. CC: Analytical Thought.
MATH-231 Foundations of Analysis
A rigorous study of the theoretical basis of single-variable differential and integral calculus: limits, continuity, differentiation and integration. Prerequisite: MATH-112 Calculus II and MATH-221 Discrete Structures. 2 SH.
MATH-235 Artificial Life
Science and mathematics describe natural phenomena so well that lines between real-world events and the corresponding theoretical-world events have become blurred. Can computer models simulate key characteristics of life, such as behavior, motivation, reproduction, adaptation, perception and even intelligence? Proponents of strong artificial life believe that computers will eventually serve not only to model life processes but will actually think and be alive. These contentions are compared and contrasted with an emphasis on the current status and future implications of strong artificial life. This course is meant to be accessible to both majors and nonmajors. Same as CSCI-235. Prerequisites: Sophomore standing and, to facilitate an elevated level of class discourse, completion of at least two of the following Central Curriculum requirements: Analytic Thought, Scientific Explanations or Ethics. 4 SH. CC: Ethics Intensive, Interdisciplinary.
MATH-321 Abstract Algebra
A more detailed study of algebraic structures. Introduces fundamental concepts of groups, rings and fields. Prerequisites: MATH-201 Linear Algebra and MATH-221 Discrete Structures. 4 SH. CC: Writing Intensive.
A concentrated study of elementary geometry. Includes Euclidean and non-Euclidean geometries and selected topics such as symmetry, Penrose tilings, fractals, knots, mapmaking and the shape of the universe. Prerequisites: MATH-201 Linear Algebra and MATH-221 Discrete Structures. 4 SH.
MATH-351 Numerical Computing
An introduction to the computational techniques for solving mathematical problems. Topics include roots of nonlinear equations, interpolation, numerical differentiation and integration, and numerical solutions of differential equations. Same as CSCI-351. Prerequisite: MATH-111 Calculus I; MATH-112 Calculus II is suggested. 2 SH.
MATH-352 Numerical Analysis
A theoretical study of the standard numerical techniques for solving mathematical problems. Topics include roots of nonlinear equations, polynomial interpolation, solving systems of equations, numerical integration and numerical solutions of differential equations. Same as CSCI-352. Prerequisites: MATH-112 Calculus II, MATH-201 Linear Algebra and MATH-351 Numerical Computing. 2 SH.
MATH-353 Differential Equations
Introduces theory, basic solution methods, qualitative analysis and applications of ordinary differential equations. Prerequisites: Sophomore standing, MATH-112 Calculus II and MATH-201 Linear Algebra or instructor's permission. 4 SH.
MATH-355 Operations Research
Mathematical models and optimization techniques useful in decision making. Includes linear programming, game theory, integer programming, queuing theory, inventory theory, networks and reliability. Further topics, such as nonlinear programming and Markov chains, as time permits. Same as CSCI-355. Prerequisites: MATH-112 Calculus II, MATH-201 Linear Algebra, MATH-221 Discrete Structures, and either MATH-108 Introduction to Statistics or MATH-180 Statistical Methods or instructor's permission. 4 SH.
MATH-370 Cryptology and Number Theory
Cryptology is the study of hiding the meaning of messages. Cryptology is an interesting venue for the study of its mathematical underpinnings (number theory, matrix algebra, probability and statistics) and as an opportunity to implement techniques by means of computer programs. We consider monoalphabetic and polyalphabetic encryptions, public key cryptography, security, and anonymity. Same as CSCI-370. Prerequisite: MATH-221 Discrete Structures. 4 SH.
MATH-411 Real Analysis
A deeper look at the fundamentals of calculus. Real numbers, point set theory, limits and the theory of continuity, differentiation, and integration. Prerequisites: MATH-112 Calculus II and MATH-221 Discrete Structures. 4 SH.
MATH-415 Complex Analysis
Calculus using complex numbers. Includes power series, analytic functions, poles, residues, contour integrals and applications. Prerequisites: MATH-211 Multivariate Calculus and MATH-221 Discrete Structures. 4 SH.
MATH-441 Mathematical Statistics
A more detailed study of statistics. Topics include probability, multivariate distributions, Bayes' Theorem, statistical inference, estimation, decision theory, hypothesis testing, linear models and experimental design. Prerequisites: MATH-211 Multivariate Calculus and either MATH-108 Introduction to Statistics or MATH-180 Statistical Methods. 4 SH.
MATH-482 Theory of Computation
An introduction to the classical and contemporary theory of computation. Topics include the theory of automata and formal languages, computability by Turing machines and recursive functions, computational complexity, and possibly quantum computers. Same as CSCI-482. Prerequisites: MATH-221 Discrete Structures and CSCI-281 Data Structures. 2 SH.
MATH-500 Senior Colloquium
Experience in individual research and presentation of topics in mathematics. The one-semester-hour version culminates in a presentation to an audience of faculty and students. The two-semester-hour version also includes a paper. Prerequisite: Senior major or department permission. 1 or 4 SH. The 4 SH version satisfies the capstone requirement. CC: Oral Intensive for the 4-SH.
MATH-501 Topics in Mathematics
Subject depends on students' and instructor's interests. Possibilities include number theory, set theoretic foundations of mathematics, topology, graph theory, differential geometry and applied mathematics. Whether the course counts as a 400-level course for majors will be announced along with the course description. Prerequisite: Instructor's permission. 2 or 4 SH.
MATH-502 Independent Study
Individual work for capable students under faculty supervision. Scheduled courses are approved for independent study only under extraordinary circumstances. Whether the course counts as a 400-level course for majors will be decided on an individual basis. Prerequisite: Department approval and instructor's consent. 2 or 4 SH.
MATH-503 Independent Research
A research project leading to a substantive paper on a selected topic in mathematics. By arrangement with a department instructor. Prerequisites: Junior or senior standing and department permission. 2 or 4 SH.
MATH-599 Mathematics Internship
Full-time mathematics-related employment at an industrial firm or a public service organization. Prerequisites: Senior standing, appropriate mathematics background courses and department internship coordinator's permission. S/U grade. 2, 4 or 8 SH.
Secondary Teaching. Coursework required by the state of Pennsylvania for admission to the teacher certification program includes successful completion of ENGL-100 Writing and Thinking or equivalent course, at least 3 semester hours in British or American literature, at least 6 semester hours of mathematics coursework (or other courses which satisfy the Central Curriculum Analytical Thought requirement), and at least one 40-hour externship.
Education course requirements for secondary education are EDUC-101 Introduction to Education and Society, EDUC-102 Historical and Philosophical Foundations of Education, EDUC-250 Educational Psychology, EDUC-260 Introduction to Special Education, EDUC-270 Instruction of Exceptional Students, EDUC-330 Technology in Education, EDUC-350 English Language Learners: Theory and Instruction, EDUC-380 Instructional Design, EDUC-423 Methods of Curriculum, Instruction, and Assessment in Teaching Mathematics, EDUC-479 Principles of Learning and Teaching in Secondary Education, EDUC-483 Differentiated Instruction and Classroom Management in Secondary Education, and the EDUC-500 Student Teaching package (EDUC-501, EDUC-502, EDUC-503, and EDUC-600).
In addition, secondary education mathematics students complete all of the usual requirements for the mathematics major. They must satisfy the "one 300-level or above mathematics course" requirement by taking MATH-331 Geometry.
Interdisciplinary Options. Mathematics majors can easily complete a minor in another department. Areas such as accounting, business, computer science, biology, chemistry, physics or a foreign language are natural choices. The department also sponsors a business-related minor in actuarial science.
Highly motivated students whose interests cross traditional departmental lines may also consider a self-designed major. This option provides an integrated program of study from courses in several departments and is described in the majors and minors section.
Central Curriculum Capstone. The Central Curriculum capstone requirement may be satisfied by the four-semester-hour version of MATH-500 Senior Colloquium. Students need not fulfill the Central Curriculum capstone requirement in their major, but they usually do.