Department of Mathematics

view dept. website http://www.houghton.edu/math/

Rebekah B. Johnson Yates, chair | Mark E. Yuly, Interim Area Associate Dean

585.567.9280
Overview

The mathematics major comprises coursework in mathematical concepts and computation with growing attention to the centrality of mathematical reasoning and proof. The major prepares students to work both collaboratively and independently and develops facility with both oral and written communication of mathematics. This combination of content, reasoning, and communication skills prepares students for a wide variety of vocations, including careers in education, industry, actuarial science, finance, computer science, health professions, and linguistics. Many students pursue advanced degrees in diverse areas such as mathematics, applied mathematics, education, architecture, law, health professions, and computer science. 

Teaching Mathematics - Inclusive Childhood (elementary) or Adolescence (secondary). See Education.

Faculty
Brandon BateJason BintzJill E. Jordan Rebekah B. Johnson Yates
Courses
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MATH 111 Math for the Liberal Arts

4-F, S

A survey course intended to introduce students to several ideas of mathematics, their historical context, and their applications and significance in society. The course will cultivate an appreciation of the significance of mathematics and develop student’s mathematical reasoning through selected topics in logic, set theory, probability, statistics, number theory, graph theory, the real number system, and problem solving. Creation: Math. Liberal Arts.

MATH 115 Fundamentals of Calculus

4-WSP

A problem-based approach to the basic ideas of calculus, beginning with a discussion of topics that precede calculus, including linear functions and polynomials. The calculus portion discusses velocity, tangent lines, and areas. Incorporates peer group work with a strong emphasis on graphing technology. With this course, students will become acquainted with calculus, the math that helped create the industrial revolution and is the driving force behind modern technology. This course is not intended to prepare students for Calculus I, but rather to expose students who do not need a rigorous course to the ideas of calculus. Creation: Math. Liberal Arts.

MATH 131 Principles of Statistics

4-S

This course introduces students to basic concepts and applications of probability theory and statistics. Students will learn how to collect, describe, understand, use, and interpret data in meaningful ways. Topics will include sampling procedure & bias, summary statistics, graphical displays, probability and probability distributions, statistical inference, correlation and linear regression. This course does not satisfy requirements for any major. Creation: Math. Liberal Arts.

MATH 170 Calculus I with Pre-calculus A

4-F

Together with MATH 171 Calculus I with Pre-calculus B, this course covers all the material of MATH 181 Calculus I with integrated treatment of pre-calculus topics. Expected calculus topics include limits, continuity, and the Intermediate Value Theorem; the theory and computation of differentiation of algebraic and trigonometric functions and applications of differentiation including tangent lines and related rates. Pre-calculus topics to support these topics will be addressed as needed. Students who received an SAT Math score of 550 or lower or equivalent who need to take Calculus I must complete this course. Enrollment by permission only. Creation: Math. Liberal Arts.

MATH 171 Calculus I with Pre-calculus B

4-S

Together with MATH 170 Calculus I with Pre-calculus A, this course covers all the material of MATH 181 Calculus I with Integrated treatment of pre-calculus topics. Expected calculus topics include applications of derivatives including optimization, curve-sketching, and the Mean Value Theorem; introduction to Integration, including the Fundamental Theorem of Calculus, computation of areas, and the technique of substitution; calculus of transcendental functions, Pre-calculus, computation of areas, and the technique of substitution,; calculus of transcendental functions. Pre-calculus topics to support these topics will be addressed as needed. Students who complete this course with a C have fulfilled the pre-requisite for Calculus II. Creation: Math. Liberal Arts.

Prerequisite Courses: MATH 170

MATH 181 Calculus I

4-F

A first semester of single variable calculus including limits, continuity, and the Intermediate Value Theorem; theory and computation of differentiation of algebraic, trigonometric, and transcendental functions; applications of derivatives including optimization, curve-sketching, related rates, and the Mean Value Theorem, introduction to integration, including the Fundamental Theorem of Calculus, computation of areas, and the technique of substitution. Prerequisites: Students must have an SAT Math score higher than 550 or equivalent, or permission of the instructor. Students who have completed MATH 171 cannot take this course. Creation: Math. Liberal Arts.

MATH 182 Calculus II

4-F&S

A second semester of single variable calculus including derivatives of all transcendental functions and L’Hospital’s rule; theory and techniques of integration including substitution, parts, trigonometric substitution, partial fractions, and improper integrals, applications of integrals including area, volume, arc length, and surface areas; sequences and series, including Maclaurin and Taylor series; basic calculus for parametric equations and polar coordinates. Prerequisite: MATH 171 or MATH 181. Creation: Math. Liberal Arts.

MATH 210 Introduction to Proofs

2-F

Introduces the central idea of proof in mathematics and some standard proof formats that are used throughout the math major. The course includes propositional logic, an introduction to predicate logic, direct proof, proof by contradiction, and mathematical induction. Prerequisite: MATH 171 or MATH 181. Liberal Arts.

MATH 214 Discrete Mathematics

2-F15

Introduction to discrete mathematical topics: equivalence relations, partial orders, functions, recurrence relations, counting, introduction to probability, graphs, and introduction to algorithm analysis. Liberal Arts.

Prerequisite Courses: MATH 210

MATH 225 Multivariate Calculus

4- F15, S17

Space geometry, vectors, vector function, function of several variables, partial differentiation, multiple integration. Liberal Arts.

Prerequisite Courses: MATH 182

MATH 241 Differential Equations

4-S16, F16

Methods of solution and applications of principle types of differential equations. Liberal Arts.

Prerequisite Courses: MATH 182

MATH 261 Linear Algebra

4-S

Linear algebra: systems of linear equations, vector spaces, linear mappings, inner products, and matrices. Prerequisite: MATH 171 or MATH 181. Liberal Arts.

Prerequisite Courses: MATH 181 , MATH 171

MATH 281 History of Mathematics

4-WSP

A contextual study of the history of mathematics and some of the classical problems. Liberal Arts.

Prerequisite Courses: MATH 182

MATH 295, 296; 395, 396; 495 Special Topics in Mathematics

1, 2, 3, or 4-

Previous topics include: graph theory; knot theory; number theory; linear algebra II. Liberal Arts.

MATH 325 Real Analysis I

4-S

This course develops a rigorous foundation for the fundamental topics covered in calculus: continuity, differentiability, integrability, and convergence based on limits and the axioms of the real number system. Liberal Arts.

Prerequisite Courses: MATH 182 , MATH 210, MATH 261

MATH 331 Numerical Analysis

4-WSP

Representation of numeric data. Error analysis, mathematical basis, and limitations of techniques relating to selection of method. Topics: linear and nonlinear systems, curve fitting, numerical calculus, programming in MatLab. Liberal Arts.

Prerequisite Courses: MATH 182 , MATH 261 , CSCI 211

MATH 333 Probability and Statistics I

4-F15

This course introduces students to discrete and continuous probability, including conditional probability, random variables, independence, Bayes’ Theorem, expected value, variance, distributions, and the Central Limit Theorem. Using the probability covered in the first half of the semester, the course also covers some of the main topics of mathematical statistics, including statistical hypothesis testing, errors, correlation, regression equations, and analysis of variance. Co-requisites: MATH 210 and MATH 225. Liberal Arts.

MATH 341 Mathematical Modeling

4-S16, F16

A course designed to develop an appreciation for and an understanding of the mathematics of complex systems. Particular problems from the life sciences and social sciences illustrate the principles and process of mathematical modeling and motivate the development of tools and techniques employed throughout applied mathematics. Liberal Arts.

Prerequisite Courses: MATH 241

MATH 351 Modern Geometries

4-S17

A survey of geometry including advanced Euclidean geometry and an introduction to non-Euclidean geometries. Liberal Arts.

Prerequisite Courses: MATH 182 , MATH 210

MATH 361 Abstract Algebra I

4-F

Groups and subgroups, rings and ideals, fields, homomorphisims, and isomorphisms. Liberal Arts.

Prerequisite Courses: MATH 210, MATH 261

MATH 380 Mathematics Research Seminar

1-S

This course introduces students to the experience of mathematics research. Each student will be part of a team working with a faculty member on an open problem. This course may be repeated multiple times for credit. Liberal Arts.

Prerequisite Courses: MATH 210

MATH 391, 392; 491, 492 Independent Study

1, 2, 3 or 4-

Liberal Arts.

MATH 393 Summer Collaborative Research in Mathematics

1, 2, 3, or 4-Summer

Summer research in collaboration with a mathematics faculty member, focusing on a current area of mathematical research. Students work intensively with a faculty member over the course of four weeks during the summer. Prerequisites will be according to the chosen area of research. Liberal Arts.

MATH 425 Real Analysis II

2-4-WSP

This course covers selected topics from real and functional analysis, building on the foundation from Real Analysis I. Liberal Arts.

Prerequisite Courses: MATH 325

MATH 433 Probability and Statistics II

2-4-WSP

This course covers topics selected from parametric and non-parametric hypothesis testing, ANOVA, partial and multiple correlation methods, regression, curve fitting, and Monte Carlo simulation. Liberal Arts.

Prerequisite Courses: MATH 333

MATH 452 Point Set Topology

4-WSP

Open and closed sets. Connected, compact, and metric topological spaces. Liberal Arts.

Prerequisite Courses: MATH 261

MATH 461 Abstract Algebra II

2-4-WSP

A continuation of material from Abstract Algebra I. Topics may include advanced group theory and ring theory, Sylow theorems, modules and vector spaces, Galois theory, and finite fields. Liberal Arts.

Prerequisite Courses: MATH 361

MATH 471 Complex Analysis

4-S16

Complex number system, limits, differentiation and integration in the complex plane, complex series. Prerequisites: courses listed below or permission. Liberal Arts.

Prerequisite Courses: MATH 225 , MATH 325

MATH 482 Senior Capstone: Mathematics Seminar

4-S

A capstone course which draws on many other courses. Emphases on formulating, solving, and explaining challenging problems in both verbal and written form. For seniors, except by permission. Liberal Arts.

MATH 496 Honors in Mathematics

4-wsp

Liberal Arts.

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