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Course Listings
Mathematics
A major and a minor in Mathematics are available, as well as teacher certification in Mathematics Education for grades 5-12.
Major in Mathematics
35 credit hours
- MATH 205 Discrete Mathematics3
- MATH 211 Calculus I4
- MATH 212 Calculus II4
- MATH 213 Multivariate Calculus4
- MATH 301 Linear Algebra3
- MATH 302 Abstract Algebra3
- MATH 305 Modern Geometry3
- MATH 321 Differential Equations3
- MATH 323 Probability and Statistics3
- MATH 390 Problem Solving Seminar1
- Choose one of the following3
- Choose one of the following1
Student Learning Outcomes
Graduates with a major in Mathematics will:
- Demonstrate knowledge of calculus, discrete structures, deductive reasoning, programming, and a selection of more advanced concepts and techniques.
- 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.
- Learn mathematics by reading, listening, exploring, and conversing in an effective manner.
- Explain and critique mathematical reasoning through speaking and writing in a precise and articulate manner in both informal and formal settings.
- Exhibit curiosity, playfulness, creativity, confidence, perseverance, interest in multiple perspectives, and a collaborative spirit.
- Describe and value interconnections among different areas and levels of mathematics, other disciplines, history, ethics, careers, and society.
Planning and Advising Notes
Students seeking teacher certification in mathematics for grades 5-12 should choose Educ 405, Student Teaching in mathematics and Math 412, Seminar: Connections. Students planning on graduate study in mathematics should take Math 311, Real Analysis, and engage in a summer research program.
Planning Guide
| First Year | Goshen Core Calculus I, II At least one of these: - Discrete Mathematics - Multivariate Calculus |
| Second & Third Years | Goshen Core Finish 200-level courses Upper-level math SST |
| Fourth Year | Balance of Goshen Core Balance of major Senior Project/Internship or Student Teaching Senior Seminar |
Minor in Mathematics
19 credit hours
- Any mathematics courses numbered 200 and above11
- Any mathematics courses numbered 300 or above8
Student Learning Outcomes
Graduates with a Mathematics Minor will:
- Demonstrate knowledge of a variety of mathematical techniques.
- Solve pure and applied programs and explore ideas by using mathematical concepts and techniques, problem solving heuristics, pattern recognition, deduction, simulation, modeling, data analysis, and/or software tools.
- Learn mathematics by reading, listening, exploring, and conversing in an effective manner.
- Explain and critique mathematical reasoning through speaking and writing in a precise and articulate manner in both informal and formal settings.
- Exhibit curiosity, perseverance, and a collaborative spirit.
EDUC 405 Student Teaching:Secondary
At least 13 weeks of full-day student teaching in a secondary school under the supervision of a teacher licensed in the student teacher’s major teaching area and a GC faculty member. Includes several workshops on campus to reflect on important...
MATH 205 Discrete Mathematics
An introduction to mathematical thinking and reasoning. Topics include number systems and arithmetic, logic and Boolean algebra, functions and relations, set theory, algorithms, combinatorics and probability, matrices, and elementary graph theory. An emphasis is placed on problem solving and proof...
MATH 211 Calculus I
Concepts of calculus emphasizing applications in the natural and social sciences. Topics include differential calculus of one and two variables and integration. Prerequisites: three and one-half units of high school mathematics including trigonometry, Math 170, or a minimum ALEKS score...
MATH 212 Calculus II
Theory and applications of single variable calculus with an emphasis on writing clear explanations and proofs. Topics include real numbers, limits, derivatives, integrals, antidifferentiation techniques, function approximation, sequences, and series. Prerequisite: A grade of C or higher in Math 211...
MATH 213 Multivariate Calculus
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, and Green’s Theorem. Prerequisite: Math 211.
MATH 301 Linear Algebra
Linear systems of equations, vector spaces, linear transformations, matrices, determinants, eigenvalues and eigenvectors, inner products, computational aspects, and applications. Prerequisite: Math 211 and either Math 205 or 212.
MATH 302 Abstract Algebra
An introduction to algebraic structures such as groups, rings and fields. Prerequisite: Math 211 and either Math 205 or 212.
MATH 305 Modern Geometry
A survey of various geometries such as constructive, axiomatic, Euclidean, coordinate, projective, transformational, hyperbolic, elliptical, and fractional dimension.
MATH 321 Differential Equations
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
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 390 Problem Solving Seminar
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 Project/Internship
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
A brief survey of the history of mathematics. Prerequisite: Junior of Senior standing.
MATH 412 Seminar:Connections
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
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.