| Mathematics
Courses
Courses with * fulfill General
Education requirements
(A-AP) = Arts - Applied
(A-TH) = Arts - Theoretical/Historical
(A-AR) = Analytical - Abstract
Reasoning
(A-QR) = Analytical - Quantitative
Reasoning
(CP) = Comparative Practices
(D-D) = Diversity - Domestic
(D-I) = Diversity - International
(D-L) = Diversity - Language
(ES) = Earlham Seminar
(IP) = Interpretive Practices
(SI) = Scientific Inquiry
(W) = Wellness
(AY) = Offered in
Alternative Year |
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*MATH 120 ELEMENTARY STATISTICS (3 credits)
Topics include exploratory data analysis; measures of central tendency, dispersion and correlation; nonparametric methods; confidence intervals; hypothesis tests; and the design of statistical studies. Also listed as MGMT 120. (A-QR)
*MATH 130 SYMBOLIC LOGIC (3 credits)
The study of formal, deductive logic emphasizing the methods for demonstrating the validity of arguments. Includes truth functional propositional logic and quantification theory through the logic of relations. Also listed as PHIL 130. (A-AR)
*MATH 150 EARLHAM SEMINAR (4 credits)
Offered for first-year students.
Topics vary. (ES)
*MATH 180 CALCULUS A (5 credits)
Calculus is the mathematical study of quantities that change with time and of areas and volumes. Amazingly, these two problems are intimately related. The development of calculus is one of the great discoveries of humanity, and the resulting discipline is of fundamental importance not only for students of the natural sciences, but also for anyone intending to do graduate work in the social sciences. MATH 180 is an introduction to the major issues in calculus: functions, limits, derivatives and integrals. It ends with the fundamental theorem of calculus, which relates areas to rates of change. (A-AR, A-QR)
*MATH 190 DISCRETE MATHEMATICS (3 credits)
Provides an introduction to college mathematics and emphasizes the process of mathematical discovery and the use of proofs to validate discoveries. Topics include number theory, graph theory, counting, set theory, logic and induction. (A-AR)
MATH 195 MATH TOOLKIT (2 credits)
An introduction to the principal topics in mathematics needed by a Computer Science major. Many of these topics are also of importance to majors in Mathematics. Topics include writing numbers in various bases, set theory, proof by induction, relations and functions, logic, matrices, complex numbers, recursion and recurrences, and rates of growth of various functions.
*MATH 280 CALCULUS B (5 credits)
A continuation of MATH 180, including techniques of integration, applications of the definite integral, infinite sequences and series and elementary differential equations. Prerequisite: MATH 180. (A-AR, A-QR)
MATH 288 SOPHOMORE SEMINAR (2 credits)
A transition into the upper-level study of mathematics. Strong emphasis on how to read mathematics at a variety of levels, and on how to write proofs and present mathematics clearly and correctly. Specific topics vary; set theory is a regular part of the seminar. Prerequisite: MATH 190.
*MATH 300 STATISTICS (3 credits)
Topics include exploratory data analysis; measures of central tendency, dispersion and correlation; nonparametric methods; confidence intervals; inference testing; probability distributions; and the design of statistical studies. Prerequisite: Math 180. (A-QR)
*MATH 310 LINEAR ALGEBRA (3 credits)
Topics include matrices, vector spaces, linear transformations and their applications. Prerequisite: MATH 280. (A-AR)
*MATH 320 DIFFERENTIAL EQUATIONS (3 credits)
Topics include the standard exact and approximate methods for solving ordinary differential equations. Prerequisite: MATH 280. (A-AR, A-QR)
*MATH 345 LOGICAL SYSTEMS (3 credits)
A second course in logic, the properties of formal systems and the metatheory of standard first-order logic. Focuses on axiomatics, proof theory and the important limitative results of the 20th century, including Gödels
theorems. Prerequisites: MATH 130 or PHIL 130. Also listed as PHIL
345. (A-AR) (AY)
*MATH 350 MULTIVARIATE CALCULUS (4 credits)
An extension of the methods of calculus to functions of more than one variable, or functions returning vectors. Issues addressed include the theory and application of partial derivatives and multiple integrals, as well as the theorems of Green, Gauss and Stokes which represent multivariate analogues of the Fundamental Theorem of Calculus. Prerequisite: MATH 280. (A-AR, A-QR)
*MATH 360 APPLIED MATHEMATICS/THEORETICAL PHYSICS (3 credits)
Students learn the application of mathematical techniques to the study of physical systems. Examines vector analysis, complex variables, Fourier series and boundary value problems. Prerequisites: MATH 320 and 350. Also listed as PHYS 360. (A-AR, A-QR)
*MATH 420 ABSTRACT ALGEBRA A (3 credits)
An introduction to modern algebra. Focuses on groups and homomorphisms; also covers rings and fields. Prerequisites: MATH 288 and 310. (A-AR)
*MATH 425 ABSTRACT ALGEBRA B (3 credits)
A continuation of Abstract Algebra A and treatment of a more advanced algebraic topic. Typical themes include ring theory, finite field, Galois theory and group representation. Prerequisite: MATH 420. (A-AR) (AY)
*MATH 430 ANALYSIS A (3 credits)
A careful and theoretical study of the real numbers and their functions. Topics include the topology of the real numbers, (uniform) continuity, (uniform) convergence and theorems involving the derivative and integral. Prerequisites: MATH 280 and 288. (A-AR)
*MATH 435 ANALYSIS B (3 credits)
A continuation of Analysis A and treatment of a more advanced analytic
topic. Typical themes include the calculus of functions of a
complex variable, functional analysis, measure theory and alternatives
to the real numbers like the P-adics, the nonstandard reals and Conway's
numbers. Prerequisite: MATH 430. (A-AR) (AY)
*MATH 482 TOPICS (3 credits)
Topics vary and may include combinatorics, number theory, history and philosophy of mathematics, linear and dynamic programming, fractals and chaos, numerical analysis, probability, topology, symbolic and algebraic computation, non-Euclidean geometry and statistics. (A-AR)
MATH 486 COMPREHENSIVE INDEPENDENT STUDY (1 credit)
A student-led seminar in which students prepare to take their
comprehensive examination. Meets several times with the supervising
faculty member, but students are responsible for directing the preparation's
focus. The grade for the course is the grade on the comprehensive exam.
Offered Spring Semester. Prerequisites: MATH 420 and 430.
MATH 488 SENIOR CAPSTONE EXPERIENCE (1 credit)
Individual and collective investigations into topics of common
mathematical interest not covered in the department's regular
course offerings. Culminates in the preparation and presentation of an
hour-long talk and accompanying paper on a mathematical topic chosen
by the student in consultation with the faculty. Offered Fall Semester.
Co-requisites: MATH 420 and 430. |
