Course details

Mathematics

David Housman, Professor of Mathematics and Computer Science
Ron Milne, SST Leader Senegal
Patricia Oakley, Department Chair, Professor of Mathematics

Introduction

The mathematics department offers a major and minor and collaborates with the computer science department on a combined major.

A satisfactory score on a competency test (or equivalent) is required before taking any mathematics course for credit at Goshen College. 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 the mathematics department Web site at www.goshen.edu/math.

Career and postgraduate opportunities

Graduates with mathematics majors are currently working in education, administration, computer technology, insurance, statistics, overseas development, mass communication 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 302, Math 305, Math 323, Math 390 or 351, and a teaching internship with Math 131 or 132. Also required are 30 credits of education courses, including a semester of student teaching. PJCS 210 is required for general education. 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

43-46 credit hours

  • CoSc 200, Programming Techniques 3
  • Math 205, Discrete Mathematics 3
  • Math 211, 212, 213, Calculus I, II & III 12
  • Math 300, Conjecture and Proof 3
  • Math 301, Linear Algebra 3
  • One of the following courses: 3
    Math 302, Abstract Algebra
    Math 305, Modern Geometry
    Math 311, Real Analysis
  • Electives in Mathematics (see note below) 12
    Any of the three courses in the previous category
    Math 321, Differential Equations
    Math 323, Probability and Statistics
    Math 341, Numerical Analysis
    Math 351, Mathematical Modeling
    Math 390, Problem Solving Seminar
    Math 400, Selected Topics
    Math 409, Senior Project/Internship
  • Science elective: Biol 111/112, Chem 111, or Phys 203/204 4
  • CoSc 410 or Phys 410, Senior Seminar 3

Planning and advising notes

12 credit hours of Math electives are required for most majors; only 9 credit hours are required for those who complete student teaching in math education.

Planning guide

First year General education
Discrete Mathematics
Calculus I, II, III
Programming Techniques
General Physics
Second year General education
Conjecture and Proof
Linear Algebra
Upper-level math
SST (summer)
Third year General education
Upper-level math
SST (fall or summer)
Fourth year Balance of general education
Balance of major
Senior Project/Internship or Student Teaching
Senior Seminar

Minor in mathematics

19 credit hours

  • Math 205, Discrete Mathematics 3
  • Math 211, 212, Calculus I & II 8
  • Elective upper level mathematics courses (300 and above) 8

Planning and advising notes

A typical way to complete upper level mathematics requirements for the minor is to take Math 300, 301 and 351.

Major in computer science and applied mathematics

A combined major in computer science and applied mathematics is available. For a full description, see computer science.

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 110 Mathematical World 3
A survey of selected content chosen to help build basic number sense, develop skills in pattern recognition, use mathematical modeling to represent and investigate practical problems. Basic arithmetic computational skills are assumed. Prerequisite: general education mathematics competency requirement.

MATH 120 Intermediate Algebra 4
Basic algebra as preparation for Math 141 or Math 170. Prerequisite: one unit of high school algebra or Math 105; and general education mathematics competency requirement.

MATH 131 Math Concepts Elem Classroom I 4
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. Prerequisite: general education mathematics competency requirement.

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. Prerequisite: Math 131 or high school geometry; general education mathematics competency requirement.

MATH 141 Finite Mathematics 3
Mathematics useful for solving problems from business and social sciences. Topics include linear systems of equations and inequalities including linear programming set theory, elementary counting principles, probability, Markov chains, financial mathematics. Prerequisite: Two units of high school algebra or Math 120.

MATH 170 Precalculus Mathematics 4
Symbolic, graphical, numerical, and verbal representations of functions and their applications. Graphing calculators and computer software are used. (Includes weekly computer lab.) Prerequisite: Three units of high school algebra and geometry or Math 120.

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. Prerequisites: three and one-half units of high school mathematics including trigonometry or Math 170.

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. Topics include limit definition of the derivative and integral; exponential, logarithmic, inverse trigonometric, and hyperbolic functions; techniques of integration; differential equations; sequences and series; an introduction to functions of several variables. (Includes weekly computer lab.) Prerequisite: Math 211.

MATH 213 Calculus III 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 212.

MATH 300 Conjecture and Proof 3
An introduction to the exploration and formalization of mathematical phenomena, techniques of proof and the rudiments of logic, sets, real analysis, and axiomatic geometry. Provides a preparation for the study of abstract mathematics. Prerequisite: Math 211 and either Math 205 or Math 212, or permission of instructor.

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 Math 212.

MATH 302 Abstract Algebra 3
An introduction to algebraic structures such as groups, rings and fields. Prerequisites: Math 300 and Math 301.

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. Prerequisites: Math 300.

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 213 or Math 301.

MATH 323 Probability and Statistics 3 (3-4)
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. The optional fourth credit hour consists primarily of an independent data collection and analysis project. Prerequisites: Math 213 or permission of the instructor.

MATH 341 Numerical Analysis 3
Numerical methods and error analysis for approximating solutions of mathematical problems. Includes linear and nonlinear numerical methods, interpolation and approximation techniques, numerical differentiation and integration. Prerequisite: CoSc 200 and one of Math 301 or Math 321.

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: CoSc 200 and one of Math 213, Math 301, or Math 323.

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 300 or permission of instructor.

MATH 400 Selected Topics: 3 (1-3)
For mathematics majors with consent of the department. May be repeated.

MATH 409 Senior Project/Internship 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.

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