At Earlham, we strive to teach our students mathematical fundamentals and problemsolving skills that they can apply in a variety of disciplines or in further study of mathematics. We work to help students become a part of the intellectual and cultural community of mathematicians. We do this by supporting them in doing research either here or in summer Research Experience for Undergraduates programs. We also do it by encouraging them to take part in mathematical competitions, to enjoy activities like our Pi Day and Celebration of the Mind events, to learn from special lectures and lunchtime conversations about math, and to be a part of the supportive and stimulating community of people working in the Math Studio.
The Association for Women in Mathematics (Careers That Count) describes mathematics as "… a powerful tool for solving practical problems and a highly creative field of study, combining logic and precision with intuition and imagination. The basic goal of mathematics is to reveal and explain patterns — whether the pattern appears as electrical impulses in an animal's nervous system, as fluctuations in stock market prices, or as fine detail of an abstract geometric figure."
A solid preparation in Mathematics can lead to a career in any field where the ability to recognize and exploit patterns is fundamental. Over the past few years, Earlham Mathematics graduates have gone on in various directions. Some are in graduate school studying applied mathematics, actuarial science, computer science, education, engineering, environmental science, law, mathematics, medicine, musicology or theology. Others have become high school teachers, business managers, computer programmers, systems analysts, environmental statisticians, actuaries or mathematics professors. Some Mathematics graduates have enrolled in Earlham College's Master of Arts in Teaching Program, while others have attended Earlham School of Religion, Indiana, Oregon State, Miami and Stanford universities and the universities of Kentucky, Michigan and Wisconsin.
General Education Requirements
The Mathematics Department offers 15 courses that fulfill the Abstract Reasoning component of the Analytical Reasoning Requirement for General Education: MATH 130, 180, 190, 280, 288, 300, 310, 320, 350, 360, 420, 425, 430, 435 and 482; and seven that fulfill the Quantitative Reasoning component of this requirement: MATH 120, 180, 280, 300, 320, 350 and 360. The Department also offers Earlham Seminars.
The Major
Students considering a major in Mathematics are encouraged to enroll in Calculus A or Discrete Math during the Fall Semester of their first year, and to discuss their plans with one of the Math faculty if they've taken calculus in high school.
Students majoring in Mathematics are required to complete:
 MATH 180 Calculus A
 MATH 190 Discrete Mathematics
 MATH 280 Calculus B
 MATH 288 Sophomore Seminar
 MATH 310 Linear Algebra
 MATH 420 Abstract Algebra A
 MATH 430 Analysis A
 Either MATH 425 Abstract Algebra B OR
MATH 435 Analysis B
 MATH 486 Comprehensive Independent Study
 MATH 488 Senior Capstone Experience
 Two other Mathematics courses numbered 300 or above
Students intending to go on in mathematics are strongly encouraged to take MATH 320, MATH 350, both MATH 425 and 435, and at least one course in Computer Science.
The Minor
 MATH 190 Discrete Mathematics
 MATH 288 Sophomore Seminar
 Either MATH 420 Abstract Algebra A OR
MATH 430 Analysis A
 Three other Mathematics courses numbered 300 or above
* Key
Courses that fulfill General Education Requirements:
 (AAP) = Arts  Applied
 (ATH) = Arts  Theoretical/Historical
 (AAR) = Analytical  Abstract Reasoning
 (AQR) = Analytical  Quantitative
 (DD) = Diversity  Domestic
 (DI) = Diversity  International
 (DL) = Diversity  Language
 (ES) = Earlham Seminar
 (IE) = Immersive Experience
 (RCH) = Research
 (SI) = Scientific Inquiry
 (W) = Wellness
 (WI) = Writing Intensive
 (AY) = Offered in Alternative Year

*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. (AQR)
*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 CS 130 and PHIL 130. (AAR)
*MATH 150 EARLHAM SEMINAR (4 credits)
Offered for firstyear 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. 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 graduate work in the social sciences. Introduces major issues in calculus: functions, limits, derivatives and integrals. Concludes with the fundamental theorem of calculus, which relates areas to rates of change. (AAR, AQR)
*MATH 190 DISCRETE MATHEMATICS (3 credits)
A course in mathematical invention and discovery. Starting with simple but unfamiliar mathematical systems, students do calculations, look for patterns, and work to convince themselves and one another of the truth of their insights as they collectively explore and develop new mathematical worlds. An early glimpse of what mathematical research is like. Strongly recommended as an introduction to college mathematics. Topics include number theory, combinatorics, set theory, logic and induction. (AAR)
MATH 195 MATH TOOLKIT (2 credits)
An introduction to the principal topics in mathematics needed by a Computer Science major, and intended for students of computer science. 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. Also listed as CS 195.
*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. (AAR, AQR)
*MATH 288 SOPHOMORE SEMINAR (3 credits)
A transition into the upperlevel 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. (AAR)
*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. (AAR, AQR)
*MATH 301 EUCLIDEAN AND NONEUCLIDEAN GEOMETRY (3 credits)
This course explores Euclid’s world of planar geometry and compares his work both to that of modern geometers and other mathematicians who did Euclidean geometry in a manner very far from Euclid’s. This course also will look at nonEuclidean geometries, where parallel lines behave in unexpected ways, and finite geometries where restrictive worlds stretch the imagination. (AAR)
*MATH 310 LINEAR ALGEBRA (3 credits)
Topics include matrices, vector spaces, linear transformations and their applications. Prerequisite: MATH 280. (AAR)
*MATH 320 DIFFERENTIAL EQUATIONS (3 credits)
Topics include the standard exact and approximate methods for solving ordinary differential equations. Prerequisite: MATH 280. (AAR, AQR)
*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. (AAR, AQR)
*MATH 360 MATHEMATICAL PHYSICS (3 credits)
Applies mathematical techniques to the study of physical systems. Examines topics such as vector analysis, complex variables, Fourier series and boundary value problems. These topics are studied in the context of modeling and understanding physical systems. Students will see how individual techniques, once developed, can be applied to very broad classes of problems. This course develops skills in communicating scientific results in written form as well as in an oral presentation. Prerequisites: MATH 320 and 350. Also listed as PHYS 360. (AAR, AQR, RCH)
*MATH 420 ABSTRACT ALGEBRA A (3 credits)
An introduction to modern algebra. Focuses on groups and homomorphisms; also covers rings and fields. Prerequisites: MATH 190, 288 and 310. (AAR)
*MATH 425 ABSTRACT ALGEBRA B (3 credits)
A continuation of MATH 420 and treatment of a more advanced algebraic topic. Typical themes include ring theory, finite fields, Galois theory and group representations. Prerequisite: MATH 420. (AAR) (AY)
*MATH 430 ANALYSIS A (3 credits)
A careful and theoretical study of the real numbers and their functions including all the details you might have asked for in Calculus A, but probably did not. Topics include the construction and topology of the real numbers, sequences of reals, limits of sequences and of functions, and (uniform) convergence and continuity. Prerequisites: MATH 280 and 288. (AAR)
*MATH 435 ANALYSIS B (3 credits)
A continuation of MATH 430 and treatment of a more advanced analytic topic. Commonly this has been a careful treatment of differentiation and Riemann integration, including results like the Fundamental Theorem of Calculus, the termwise integrability and differentiability of power series, and perhaps the theorem that a function on a closed, bounded interval is Riemann integrable if and only if it is bounded and almost everywhere continuous. Prerequisite: MATH 430. (AAR) (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, nonEuclidean geometry and statistics. (AAR)
MATH 486 COMPREHENSIVE INDEPENDENT STUDY (1 credit)
A studentled 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. Prerequisites: MATH 420 and 430. Offered Spring Semester.
MATH 488 SENIOR CAPSTONE EXPERIENCE (3 credits)
Individual and collective investigations into topics of common mathematical interest not covered in the department's regular course offerings. A significant part of this course is students' reading new mathematics and presenting it to one another. Corequisites: MATH 420 and 430. Offered Fall Semester.