Mathematics

Mathematics began with roots in the basic concepts of space and number and has flowered into many wonderful forms. The creation and discovery of new mathematics have never been more active or vital than they are today. Mathematics is sometimes called the science of pattern and order. It relies on logic as a standard of truth, but uses observation and even experimentation as means of discovering truth. Mathematicians think of their work as a blend of science and art, sometimes elegant and beautiful, describing deep and useful creations. In addition to theorems and theories, mathematics offers distinct modes of thought which are both versatile and powerful for understanding the world.

Courses serve those who wish to make mathematics a part of a liberal arts education, those who desire a mathematics background for other disciplines, such as Computer Science, Economics or the natural sciences, those who wish to minor in Mathematics, and those who wish to major in Mathematics.

Mathematics majors choose careers in education, industry, business, banking and insurance serving as teachers, statisticians, industrial mathematicians, computer programmers or analysts, actuaries and research workers in the biological, management or social sciences. Their training can also serve as a stepping stone to professional training or graduate work in a variety of fields.

Requirements for the Mathematics Major (10 Credits)

• MATH 251 (W) Foundations of Advanced Mathematics (1)
• MATH 253 (QA) Linear Algebra (1)
• MATH 499 Seminar in Mathematics (1)
• One Computer Science course at the 200 level or above (1)

Three additional credits in Mathematics at the 400 level (3), including at least one of:

• MATH 446 Real Analysis I (1) or
• MATH 456 Abstract Algebra I (1)

Three additional credits in Mathematics (3)

• One credit in Mathematics numbered 300 or above (1)
• Two credits in Mathematics numbered 200 or above (2)

Requirements For The Mathematics Minor (6 Credits)

• Five credits in Mathematics numbered 142 or higher (5)
• One course in Computer Science numbered 200 or higher (1)

Faculty

• Mark R. Janeba, Associate Professor of Mathematics
• Inga Johnson, Assistant Professor of Mathematics
• Joshua D. Laison, Assistant Professor of Mathematics
• Erin M. McNicholas, Assistant Professor of Mathematics
• Kathryn Nyman, Assistant Professor of Mathematics
• Peter T. Otto, Assistant Professor of Mathematics
• Colin L. Starr, Assistant Professor of Mathematics

Course Listings

MATH 102X Problem-Solving (.25)

The course will offer students the opportunity to solve challenging mathematical problems unlike standard homework problems in any course. Class time will be spent studying problems, discovering solutions, writing up solutions formally, and discussing the important ideas of each solution. Most problems will be of the kind appearing on the Putnam Exam, an annual international mathematics competition. This course may be repeated for credit.

• Offering: Fall
• Instructor: Staff

MATH 130 (QA*) Contemporary Mathematics (1)

A survey of contemporary topics in mathematics such as: voting systems and power, apportionment, fair division of divisible and indivisible assets, efficient distribution, scheduling and routing, growth and decay in nature and economics, symmetry and fractal geometry, probability and statistics. MATH 130 may not be taken for credit after any Mathematics course numbered above 140 has been completed.

General Studies Requirement Fulfillment: Quantitative and Analytical Reasoning (*)

• Offering: Every semester
• Instructor: Staff

MATH 138 (QA*) Statistics (1)

This course is an introduction to descriptive and inferential statistical analysis. The following topics will be examined: scales of measurement; frequency distributions; graphing data; measures of central tendency, dispersion and skewness; sampling distributions; probability distributions; the binomial, Poisson and normal distributions; hypothesis testing; confidence intervals and interval estimation; t-tests; analysis of variance; correlational analysis; regression analysis; and analysis of nominal-level data.

General Studies Requirement Fulfillment: Quantitative and Analytical Reasoning (*)

• Offering: Every semester
• Instructor: Staff

MATH 141 (QA*) Calculus I (1)

A first course in calculus-differential and integral calculus of algebraic and exponential functions, with applications. (MATH 141 counts for only .5 credit if the student has completed MATH 139 Brief Calculus.)

General Studies Requirement Fulfillment: Quantitative and Analytical Reasoning (*)

Prerequisite: Placement exam required (high school math beyond Algebra II recommended)

• Offering: Every semester
• Instructor: Staff

MATH 142 (QA*) Calculus II (1)

A second course in calculus: review of differential and integral calculus via trigonometric and logarithmic functions, techniques and applications of integration, polar coordinates and parametric equations, infinite series.

General Studies Requirement Fulfillment: Quantitative and Analytical Reasoning (*)

Prerequisite: MATH 141 or placement exam (previous Calculus experience required)

• Offering: Every semester
• Instructor: Staff

MATH 163 (QA*) Discrete Mathematics (1)

Introduction to basic techniques and modes of reasoning in combinatorial problem-solving. Topics will be chosen from combinatorial mathematics, logic and Boolean algebra, difference equations, graph theory and applied algebra.

General Studies Requirement Fulfillment: Quantitative and Analytical Reasoning*

• Offering: Spring
• Instructor: Staff

MATH 220 (QA) Mathematics for Elementary Teachers (1)

The objective of the course is to present mathematics in a format that prepares teachers to teach elementary school mathematics. Teachers need a firm foundation in the theory of mathematics as it pertains to the elementary school curriculum. They also need ideas and methods for teaching that will generate interest and enthusiasm among the students. Topics to be covered will include problem solving, mathematics as a method of communication, mathematics as a method of reasoning, and specifics of elementary school mathematics such as whole number operations, geometry and spatial sense, measurement and estimation, fractions and decimals, and patterns and relationships.

General Studies Requirement Fulfillment: Quantitative and Analytical Reasoning

Prerequisite: Previous or concurrent enrollment in EDUC 305 or consent of instructor

• Offering: On demand
• Instructor: Prothero

MATH 249 (QA*) Multivariable Calculus (1)

Three-dimensional analytic geometry; partial differentiation; maxima-minima problems; multiple integrals; vector fields, curl and divergence; line and surface integrals; applications.

General Studies Requirement Fulfillment: Quantitative and Analytical Reasoning (*)

Prerequisite: MATH 142

• Offering: Every semester
• Instructor: Staff

MATH 251 (W) Foundations of Advanced Mathematics (1)

This course is intended as the first course after calculus for those students intending to major or minor in mathematics. It provides an introduction to logic and the methods of proof commonly used in mathematics. Applications covered in the course are the foundations of set theory, the real number system, elementary number theory and other basic areas of mathematics.

General Studies Requirement Fulfillment: Writing centered

Prerequisite: One year of college calculus credit

• Offering: Every semester
• Instructor: Staff

MATH 253 (QA) Linear Algebra (1)

Systems of linear equations, matrices, vector spaces and linear transformations.

General Studies Requirement Fulfillment: Quantitative and Analytical Reasoning

Prerequisite: MATH 251

• Offering: Every semester
• Instructor: Staff

MATH 256 (QA) Differential Equations (1)

Elementary differential equations; linear differential equations of second order; Laplace transformations; infinite series solutions; systems of linear differential equations.

General Studies Requirement Fulfillment: Quantitative and Analytical Reasoning

Prerequisite: MATH 249. MATH 253 recommended.

• Offering: Fall
• Instructor: Staff

MATH 266 (QA*) Probability and Statistics (1)

A calculus-based introduction to probability and statistics. Topics include summary statistics, probability theory, discrete and continuous random variables, distribution, limit theorems, estimation, hypothesis testing, and linear regression.

General Studies Requirement Fulfillment: Quantitative and Analytical Reasoning (*)

Prerequisite: MATH 142.

• Offering: Spring
• Instructor: Staff

MATH 325 (QA) Mathematics for Teachers (1)

The objective of this course is to present mathematics in a format that prepares teachers to teach mathematics in the public schools. Teachers need a firm foundation in the theory of mathematics as it pertains to their particular curricula. They also need ideas and methods for teaching that will generate interest and enthusiasm among the students. The course will emphasize mathematics as a method of communication and reasoning. Topics selected to be relevant to elementary, middle, and/or high school curricula will depend on the interests of the students, but will have a strong problem-solving emphasis. The course will require an extensive early field experience in the public school classroom.

General Studies Requirement Fulfillment: Quantitative and Analytical Reasoning

Prerequisite: Previous or concurrent enrollment in EDUC 305 or consent of instructor

• Offering: On demand
• Instructor: Prothero

MATH 345 (QA) Complex Variables (1)

Complex numbers, limits, differentiation, analytic functions, integration, conformal mapping, Riemann surfaces and applications.

General Studies Requirement Fulfillment: Quantitative and Analytical Reasoning

Prerequisite: MATH 249

• Offering: Alternate years in fall
• Instructor: Staff

MATH 349 (QA) Numerical Analysis (1)

Application of numerical methods to the solution of mathematical problems. Numerical differentiation, integration and the solution of differential equations.

General Studies Requirement Fulfillment: Quantitative and Analytical Reasoning

Prerequisite: MATH 251 plus MATH 253 or MATH 256 and experience in computer programming

• Offering: On demand
• Instructor: Staff

MATH 356 (QA) Number Theory (1)

An introduction to the theory of numbers to include such topics as divisibility, congruence, diophantine equations, quadratic reciprocity, the theory of prime numbers and analytic number theory.

General Studies Requirement Fulfillment: Quantitative and Analytical Reasoning

Prerequisite: MATH 251

• Offering: Alternate years in spring
• Instructor: Staff

MATH 366 (QA) Applied Mathematics: Optimization (1)

Formulation of problems in mathematical terms, solutions of the problems, interpretation and evaluation of the solutions. Topics will be chosen from inventory problems, growth and survival models, linear programming, scheduling, Markov chains, game theory and queuing problems.

General Studies Requirement Fulfillment: Quantitative and Analytical Reasoning

Prerequisite: MATH 253 or consent of instructor

• Offering: On demand
• Instructor: Staff

MATH 376 Topics in Mathematics (1)

This course offers timely exposure to topics in mathematics which are not part of the regular curriculum. Examples of topics which might be offered: Graph Theory, Advanced Linear Algebra, Operations Research.

• Offering: Alternate Years
• Instructor: Staff

MATH 446 Real Analysis I (1)

Rigorous study of the real numbers and real-valued functions. Topics include: limits and continuity on the real line, elementary topology of the real numbers, pathological examples. Other topics may include metric spaces, differentiation, vector-valued functions.

Prerequisite: MATH 253 or consent of instructor

• Offering: Twice every five semesters
• Instructor: Staff

MATH 447 Real Analysis II (1)

A continuation of MATH 446. Topics include: Differentiation and Riemann integration, sequences of functions. Other topics may include point-set topology of the reals, vector-valued functions, topological vector spaces, Lebesgue intetration, introductory measure theory.

Prerequisite:  MATH 446

• Offering: Alternate years
• Instructor: Staff

MATH 456 Abstract Algebra I (1)

Number systems, elementary number theory, groups, rings, fields, polynomials and applications. Additional topics may be chosen from linear algebra, multilinear algebra, Sylow theory and Galois theory.

Prerequisite: MATH 253 or consent of instructor

• Offering: Alternate Years
• Instructor: Staff

MATH 457 Abstract Algebra II (1)

Course will build on the topics studies in MATH 456, Abstract Algebra I. In addition to Groups, Rings, and Fields, topics may include Galois Theory, Sylow Theory, Cayley Graphs, etc.

Prerequisite: MATH 456 or consent of instructor

• Offering: Alteranate Years
• Instructor: Staff

MATH 470 Topology (1)

Elementary point-set topology with an introduction to combinatorial topology and homotopy.

Prerequisite: MATH 251, 253 or consent of instructor

• Offering: Alternate years
• Instructor: Staff

MATH 476 Modern Geometry (1)

A modern approach to geometry. Topics will be chosen from Euclidean, non-Euclidean, affine, projective and differential geometry.

Prerequisite: MATH 253 or consent of instructor

• Offering: Twice every five semesters
• Instructor: Staff

MATH 486 Topics in Mathematics (1)

This course offers timely exposure to topics in mathematics which are not part of the regular curriculum. Examples of topics which might be offered: Cryptology, Differential Geometry, Vector Analysis, Topology.

• Offering: On demand
• Instructor: Staff

MATH 490 Independent Research (.5)

Directed research to investigate topics of special interest under the guidance of a faculty member. Topics chosen on the basis of the background and interests of the individual student.

Prerequisite: Consent of instructor

• Offering: On demand
• Instructor: Staff

MATH 491 Advanced Independent Study (.5)

A course of directed research designed to enable the exceptional student to continue the investigation of topics of special interest under the guidance of a faculty member.

Prerequisite: Consent of instructor

• Offering: On demand
• Instructor: Staff

MATH 499 (W) Seminar in Mathematics (1)

Study selected in consultation with the mathematics faculty and presented to the class. The seminar serves as the Senior Year Experience and involves oral and written presentation of research and reading topics. Required for Mathematics majors.

General Education Requirement Fulfillment: Writing-Centered

Prerequisite: Senior standing and consent of instructor

• Offering: Spring
• Instructor: Staff