Acadenics

 

Mathematics

Lisa Gautsche, Assistant Professor of Mathematics
David Housman, Department Chair, Professor of Mathematics

Introduction

The Mathematics department offers the following programs:

The study of mathematics is framed within the context of a Christian liberal arts environment that fosters critical and innovative thinking, promotes ethical awareness, views all disciplines as inter-disciplinary, develops an openness to other people and ideas, and prepares persons for a life of continued personal growth, development and learning. Visit www.goshen.edu/math for more information.

Career and postgraduate opportunities

Graduates with mathematics majors are currently working in education, administration, computer technology, insurance, statistics, finance, overseas development, operations research, and engineering.

Teacher education requirements

Teacher certification in mathematics is available for grades 5-12. Courses needed in addition to the Mathematics major core requirements are Math 301; Math 302; Math 305; Math 323; one of Math 350, 351, or 360, and a teaching internship with Math 131 or 132. Also required are 30 credits of education courses, including a semester of student teaching. The first education class, Educ 201, should be taken in May term of the first year or fall of the sophomore year. See the education department pages and the Teacher Education Handbook for more details about requirements.

Academic requirements

  • Mathematics majors must achieve a grade of C or better in every course counted for the major.
  • All students taking mathematics courses must earn a grade of C or better in prerequisite courses.

Major in mathematics

41-47 credit hours

Core Courses (23-26 credit hours)

  • Info 230, Programming I4
  • Math 205, Discrete Mathematics 3
  • Math 211-212, Calculus I & II 8
  • Math 213, Multivariate Calculus 4
  • Math 390, Problem Solving Seminar1
  • Math 409, Project/Internship0-3
  • Math 411, Seminar: History 1
  • Math 412, Seminar: Connections 1
  • Math 413, Seminar: Discoveries 1

Electives in Mathematics (18-21 credit hours) See advising note below.

    Math 301, Linear Algebra
    Math 302, Abstract Algebra
    Math 305, Modern Geometry
    Math 311, Real Analysis
    Math 321, Differential Equations
    Math 323, Probability and Statistics
    Math 350, Advanced Game Theory
    Math 351, Mathematical Modeling
    Math 355, Graph Theory
    Math 360, Biomathematics
    Math 375, Special Topics
    Up to 3 credit hours of upper level computer science or informatics courses

Student learning outcomes

Graduates in mathematics will:

  1. Demonstrate knowledge of calculus, discrete structures, deductive reasoning, programming, and a selection of more advanced concepts and techniques.
  2. Solve pure and applied problems and explore ideas by adeptly using mathematical concepts and techniques, problem solving heuristics, pattern recognition, deduction, simulation, modeling, data analysis, and software tools.
  3. Learn mathematics by reading, listening, exploring, and conversing in an effecive manner.
  4. Explain and critique mathematical reasoning through speaking and writing in a precise and articulate manner in both informal and formal settings.
  5. Exhibit curiosity, playfulness, creativity, confidence, perserverance, interst in multiple perspectives, and a collaborative spirit.
  6. Describe and value interconnections among different areas and levels of mathematics, other disciplines, history, ethics, careers, and society.

Planning and advising notes

21 credit hours of Math electives are required for most majors; only 18 credit hours are required for those who complete student teaching in math education. Math secondary education majors do a teaching internship with Math 131 or 132.

Planning guide

First year Goshen Core
Calculus I, II
At least one of these:
Discrete Mathematics
Multivariate Calculus
Programming I
Second year Goshen Core
Start upper-level math
SST
Third  year Goshen Core
Upper-level math
Problem Solving & History or Connections & Discoveries
Fourth year Balance of Goshen Core
Balance of major
Senior Project/Internship or Student Teaching
Problem Solving & History or Connections & Discoveries

Minor in mathematics

19 credit hours

  • Math 211-212, Calculus I & II 8
  • Elective upper level mathematics courses (Math 205 or any courses 300 and above)11

Math courses


MATH 105 Quantitative Reasoning 3
Emphasis on the ability to critically interpret mathematical information commonly found in public discourse and positions of responsibility and leadership. Topics will include measurement and units, proportions, estimation, simple functions, graphs and their interpretation, appropriate use of technology (e.g., spreadsheets and calculators), probability, and descriptive statistics. Examples incorporating mathematical arguments will be taken from a wide variety of fields including social science, sports, finance, environmental issues, education, and health. This course can be used to meet the general education mathematics competency requirement and is intended for students who have not met the competency requirement by exam scores or transfer credit.

MATH 115 Applied Algebra 3
An introduction to mathematical modeling using graphical, numerical, symbolic, and verbal techniques to describe and explore real-world data and phenomena. Emphasis is on the use of elementary functions to investigate and analyze applied problems and questions, supported by the use of appropriate technology, and on effective communication of quantitative concepts and results. Recommended background: two years of high school algebra and/or geometry or Math 105.

MATH 131 Math Concepts Elem Classroom I 3
Theory of natural, rational, and real number arithmetic; computation in different numeration systems; elementary set theory and logic; number theory; probability and statistics; problem solving strategies. Linkage to mathematics education in the elementary school. Recommended background: one year of high school algebra.

MATH 132 Math Concepts Elem Classroom II 3
Formal and informal approaches to Euclidean geometry; patterns, symmetries, classification of geometric figures in two and three dimensions; transformations in the plane; measures, measurement and approximate data; computer software applications to geometry. Linkage to mathematics education in the elementary school. Recommended background: one year of high school geometry.

MATH 141 Finite Mathematics 3
Mathematics useful for solving problems from business and social sciences. Topics include linear systems of equations and inequalities, linear programming, compound interest, set theory, elementary counting principles, probability, and statistics. Recommended background: three years of high school algebra and geometry or Math 115.

MATH 170 Functions, Data, and Models 4
Symbolic, graphical, numerical, and verbal representations of functions to model real-world phenomena and the use of data to fit and verify models. Recommended background: three years of high school algebra and geometry or Math 115.

MATH 201 Fair Allocation 3
This course examines the fair distribution of resources such as money, goods, voting power, and jobs. Case studies might involve dividing an estate, deciding priority for organ transplant, or creating a fair system of taxation. Allocation methods will be analyzed from mathematical, economic, political, and philosophical perspectives. A Peacemaking Perspectives course in the Goshen core. Prerequisite: Engl 105 or equivalent, quantitative literacy.

MATH 205 Discrete Mathematics 3
An introduction to mathematical thinking and reasoning. Topics include number systems and arithmetic, logic and Boolean algebra, functions and relations, set theory, combinatorics and probability, and elementary graph theory. An emphasis is placed on problem solving and proof techniques. Recommended background: four years of high school mathematics, including some calculus or Math 211.

MATH 211 Calculus I 4
Concepts of calculus emphasizing applications in the natural and social sciences. Topics include differential calculus of one and several variables, integration, mathematical modeling using differential equations. Prerequisites: three and one-half units of high school mathematics including trigonometry or Math 170.

MATH 212 Calculus II 4
A continuation of differential and integral calculus of a single variable from a theoretical perspective. Topics include limit definition of the derivative and integral; exponential, logarithmic, and inverse trigonometric, functions; techniques of integration; differential equations; sequences and series; an introduction to mathematical writing and proof. Prerequisite: Math 211.

MATH 213 Multivariate Calculus 4
Differentiation and integration of functions of two and three variables and an introduction to vector calculus. Topics include optimization, vector fields, line and surface integrals, Green's Theorem. Also includes complex variables and Fourier series. Prerequisite: Math 211.

MATH 250 Game Theory 3
Mathematical models of interactions among players: people, companies, nations, or genes. Concepts include strategy, preferences, equilibrium, efficiency, solutions, and fairness properties. Applications to biology, business, economics, politics, psychology, and theology are explored. Math 250 and Math 350 are taught simultaneously. Math 250 emphasizes modeling and application of techniques. Prerequisite: Math 170.

MATH 301 Linear Algebra 3
Linear systems of equations, vector spaces, linear transformations, matrices, determinants, characteristic vectors and values, inner products, computational aspects, and applications. Prerequisite: Math 211 and either Math 205 or 212.

MATH 302 Abstract Algebra 3
An introduction to algebraic structures such as groups, rings and fields. Prerequisite: Math 211 and either Math 205 or 212.

MATH 305 Modern Geometry 3
A survey of geometrics. Comparison of Euclidean, hyperbolic, elliptical, and projective geometries. Integral and fractional dimension; transformation groups; implications for computer graphics. Prerequisite: Math 211 and either Math 205 or 212.

MATH 311 Real Analysis 3
A rigorous study of differentiation and integration of both one and several variables. Infinite series. Distance, compactness, limits of sequences, convergence, and introduction to the topology of Euclidean n-space. Prerequisite: Math 211 and either Math 205 or 212.

MATH 321 Differential Equations 3
The solution and application of ordinary differential equations; analytic solutions for linear systems; qualitative behavior of nonlinear systems; approximation and computer methods. Prerequisite: Math 211.

MATH 323 Probability and Statistics 3
An introduction to the theory, practice and computer simulation of probability and statistics. Data exploration, sample spaces, random variables, probability distributions and their derivations, probability simulations and statistical inference. Prerequisite: Math 211 and either Math 205 or 212.

MATH 350 Advanced Game Theory 3
Math 250 and 350 are taught simultaneously. Math 350 emphasizes derivation and justification for game theory techniques. Prerequisite: Math 211 and either Math 205 or 212.

MATH 351 Mathematical Modeling 3
The modeling process, built around a study of applications from a variety of both social as well as natural sciences. A variety of mathematical and computing techniques will be employed including discrete structures, probability, calculus, differential equations and algorithms. Completion of modeling projects will be a major component of the course. Prerequisites: INFO 230, and one of Math 213, 301, 321, or 323.

MATH 355 Graph Theory 3
An introduction to the concepts and techniques of graph theory with application to diverse areas such as management, computers, circuitry, communications, and social networks. Topics covered include graphs and digraphs, paths and circuits, graph and digraph algorithms, trees, cliques, planarity, duality and colorability. Prerequisite: Math 211 and either Math 205 or 212.

MATH 360 Biomathematics 3
Mathematical models for understanding biological phenomena such as population growth, drug dosage, epidemics, genetics, and cardiac function. Skills developed include the ability to analyze an unfamiliar problem, determine the type of data needed, select the appropriate mathematical tools to be applied, and evaluate the results. Prerequisites: Biol 110, 120 or 130, Math 211; and a basic understanding of statistics.

MATH 375 Special Topics 3
Classroom study of selected topics in mathematics. Topics may include: theory of computation, cryptography, complex analysis, numerical analysis, number theory, combinatorics. May be repeated. Offered according to demand. Prerequisite: Upper-level status and consent of instructor.

MATH 390 Problem Solving Seminar 1
The problem-solving process in the context of nonroutine problems, including a wide variety of general heuristics for approaching such problems. May be repeated. Prerequisite: Math 205 or 212.

MATH 409 Senior Project/Internship 3 (0-3)
Project designed to give the student practical experience in mathematics. Each student's project is individually arranged with the instructor. Arrangements must be made at least one semester in advance.

MATH 411 Seminar:History 1
A brief survey of the history of mathematics. Prerequisite: Junior of Senior standing.

MATH 412 Seminar:Connections 1
A study of the interconnections among mathematics, other disciplines, ethics, careers, and society. Prerequisite: Math 205, 212, and two upper level Math courses.

MATH 413 Seminar:Discoveries 1
An examination of an open mathematical question and presentation of results in written and oral form. Prerequisites: Math 205, 212, and two upper level Math courses.