General Education Courses
Calculus continues to be the most common way for both science and nonscience majors to meet the Quantitative and Mathematical Reasoning requirement at Union. The following courses (051 through 061) represent alternatives that also fulfill that requirement. These courses normally are not open to students who have passed calculus courses. Note that there also are courses in computer science and philosophy that can be used to fulfill the QMR requirement.
MTH051. Cryptology: The Mathematics of Secrecy (Not offered 2014–15).
The course will focus on the mathematical aspects of publickey cryptography, the modern science of creating secret ciphers (codes), which is largely based on number theory. Additional topics will be taken from cryptanalysis (the science of breaking secret ciphers) and from contributions that mathematics can make to data security and privacy. Union Graduate College School of Engineering and Computer Science courses are available as Union College electives subject to Union College student advisor and Union Graduate College Dean, School ofMTH053. Visualizing the Fourth Dimension (Not offered 2014–15).
An investigation of the idea of higher dimensions and some of the ways of understanding them. The classic novel, Flatland, is the starting point; discussions, writing, projects and interactive computer graphics are used to extrapolate ideas from two and three dimensions to their analogues in four dimensions and higher.MTH054. Number Theory: From Clock Arithmetic to Unbreakable Codes (Fall, Spring).
An introduction to the beauty and use of numbers. Topics chosen from divisibility tests, prime numbers, perfect numbers, unbreakable codes, Fermat's theorem, the golden section, calendars, magic squares, quadratic reciprocity, and others.MTH055. Ancient Greek Mathematics (Not offered 2014–15).
Ancient Greek mathematicians invented the notion of abstraction (in mathematics and other fields), absolute precision, and proof. The approach to mathematics that we take today can be traced back to these Greek mathematicians. After examining some preGreek mathematical traditions, we study Greek mathematics, beginning with Thales and Pythagoras. Topics include the intellectual crisis caused by the discovery that not all magnitudes are commensurable; Plato and his academy; Euclid and his Elements; the three special construction problems (trisecting an angle, squaring a circle, doubling a cube); and the greatest of the Greek mathematicians, Archimedes.MTH056. History of Mathematics (Spring).
Traces the development of mathematical ideas and methods in literate cultures from ancient Egypt and Mesopotamia, to Hellenistic Greece and medieval China, India and the Islamic world, up through the dawn of calculus at the start of the Scientific Revolution in early modern Europe.MTH057. Game Theory and its Applications in the Humanities and Social Sciences (Not offered 2014–15)).
A selfcontained introduction to the mathematical theory of conflict. Examples and applications include parlor games, auctions, games from the Bible and games commenting on the existence of superior beings, gametheoretic analyses in literature, philosophical questions and paradoxes arising from game theory, and gametheoretic models of international conflict. Not open to students who have passed Math 199.MTH058. Applications of Mathematics to Economics I (Not offered 2014–15).
Linear and exponential functions, matrix algebra and linear programming with applications to the social sciences. Some sections include the use of computer spreadsheets for computations and graphical analysis. Not open to students who have passed a college calculus course.MTH059. Applications of Mathematics to Economics II (Not offered 2014–15).
Differential and integral calculus with applications in the social sciences. Students who wish to continue the calculus after Math 059 should enroll in Math 112. Prerequisite: Math 058. Not open to students who have passed a college calculus course.MTH060. Mathematics and Politics (Winter) (Same as Political Science 123).
A mathematical treatment (not involving calculus or statistics) of escalation, political power, social choice, and international conflict. No previous study of political science is necessary, but PSC 111 or 112 would be relevant.MTH061. Math in the Public Interest (Not offered 2014–15).
Explores key mathematical topics including statistics, probability, exponential and logarithmic functions, and visual/graphical representation of numbers, in the context of contemporary public policy issues such as the 2008 financial crisis, gaming institutions, population demographics, and climate change.MTH064. Statistical Thinking (Fall, Winter).
Seeks to provide the conceptual foundation and analytical skills required to understand a complex, datarich and uncertain (stochastic) world from a stochastic versus deterministic perpective, and to navigate through the daily bombardment of data from all sides.Courses
MTH100, 101, 102. Calculus with Precalculus (100 – Fall; 101 – Winter; 102 – Spring).
This sequence covers the same material as Math 110 and Math 112, but it is spread out over three terms. There is an additional emphasis placed on review of fundamental precalculus concepts. Math 100 alone does not fulfill the Quantitative and Mathematical Reasoning requirement.MTH104. Introduction to Statistics (Winter).
This course is intended to provide the conceptual foundations, and also analytical skills, for students to be able to quantify uncertainty, and further, to make rational decisions in the face of uncertainty. It addresses collection of highquality data, basic statistical analysis of such data, including use of computer software, and drawing actionable conclusions from analyses. These conclusions include understanding the limitations of statistical analyses. The integration of subject matter knowledge with data analysis within the sequential cycle of scientific inquiry will be emphasised. This course is also intended to prepare students for more advanced statistics courses, such as those in experimental design or regression analysis.MTH110. Calculus I: Differential Calculus (Fall, Winter).
Calculus of one real variable. Differentiation of algebraic functions, and applications. Not intended for students who have passed a calculus course orMTH059. MTH112. Calculus II: Integral Calculus (Winter, Spring).
Integral calculus of functions of a single variable, the fundamental theorem, formal integration and applications, calculus of logarithmic, exponential, and inverse trigonometric functions. Prerequisite:MTH110. MTH113. AP Calculus (Fall).
Selfcontained treatment of the main topics inMTH110 andMTH112. Intended for freshmen who have been introduced to (but have not yet mastered) the basics of differential and integral calculus.MTH115. Calculus III: Differential Vector Calculus and Matrix Theory (Fall, Winter, Spring).
Geometry of3space, differential calculus of functions of several variables, linear systems, matrices. Prerequisite:MTH102, MTH112, orMTH113. MTH117. Calculus IV: Integral Vector Calculus (Fall, Winter, Spring).
Double and triple integrals, line integrals and Green's theorem, divergence and curl, divergence theorem and Stokes' theorem. Prerequisite:MTH115. MTH127. Numerical Methods (Fall).
Newton's method, numerical differentiation and integration, solution of ordinary differential equations, error estimates. Prerequisites: Math 115 and fluency in some mathematical programming language.MTH128. Probability (Winter).
Probability theory and applications. Prerequisite:MTH102, MTH 112, orMTH113. MTH130. Ordinary Differential Equations (Winter, Spring).
Linear differential equations and power series. Not open to students who have passedMTH234. Prerequisite:MTH115. MTH138. Methods of Applied Mathematics I (Not offered 2014–15)
An introduction to the mathematical techniques and analysis of ordinary differential equations, partial differential equations, and complex variables. The emphasis is on the equations arising from physical, biological, and economic phenomena. Prerequisite:MTH130 orMTH234. MTH164. Strategies of Experimentation: Statistical Design and Analysis of Experiments (Winter)
Experimentation is at the heart of the scientific method, both in the physical and social sciences. Not only do experiments validate or disprove existing hypotheses, but often unexpected results lead to the development of new hypotheses and new theoretical understanding. This course will focus on strategies to accelerate the scientific method when experimenting with multiple variables. Specific topics include design options, such as simple comparative experiments, factorials and fractional factorials, and response surface designs, as well as analysis methods such as graphical methods, analysis of variance, and regression models. Familiarity with basic statistics is assumed.MTH180. Linear Algebra and Matrix Theory (Not offered 2014–15).
Vector spaces, matrices, and solutions of linear systems of equations, linear transformations, eigenvectors, and eigenvalues. Not open to students who have passedMTH340. Prerequisite:MTH115 or equivalent.MTH197. Discrete Mathematics for Computer Science (Spring).
An introduction to fundamental concepts and methods of proof in mathematics and computer science. Topics include elementary logic, functions, relations, sets, and basic combinatorics.MTH199. Introduction to Logic and Set Theory (Fall, Winter, Spring).
Designed to enable the student to develop the ability to understand and communicate mathematical arguments. Logic and set theory form the core. Selected topics are covered at the discretion of the instructor. For those considering any form of mathematics major, the department recommends that Math 199 be taken by fall term of the sophomore year, if possible. Prerequisite:MTH102, MTH112, orMTH113. MTH219. Topics in Discrete Mathematics (Fall).
Topics may include graph theory, partially ordered sets, algebraic coding theory, computational complexity, number theory. Prerequisite:MTH199 or permission of the instructor.MTH221. Mathematical Cryptology (Winter).
An indepth look at the mathematical theory underlying modern methods to accomplish the secret transmission of messages, as well as other tasks related to data security, privacy, and authentication.MTH221 normally is closed to students who have passedMTH235 orMTH051. Prerequisite:MTH199 or permission of the instructor.MTH224. Geometry (Spring).
Topics in Projective, Affine, Euclidean, and/or nonEuclidean geometries. Prerequisite:MTH199 or permission of the instructor.MTH234. Differential Equations (Winter).
Topics include systems of ordinary differential equation, series solutions, asymptotic solutions, integral equations. Not open to students who have passedMTH130. Prerequisite:MTH115 andMTH199, or permission of the instructor.MTH235. Number Theory (Fall).
Properties of natural numbers including divisibility, prime numbers, congruences, special number theoretic functions and quadratic reciprocity. Math 235 normally is closed to students who have passedMTH221. Prerequisite:MTH199 or permission of the instructor.MTH238. Methods of Applied Mathematics (Spring).
An introduction to the mathematical techniques and analysis of ordinary differential equations, partial differential equations, and complex variables. The emphasis is on the equations arising from physical, biological, and economic phenomena. Prerequisite:MTH130 or MTH234 and MTH197 or MTH199. MTH264. Regression Analysis (Spring).
Regression analysis is one of the most important and influential methods in statistics, finding application in virtually all disciplines, from business to healthcare to sociology to the hard sciences. This course will cover both the science of regression analysis  its underlying mathematical theory, as well as the art of its practical application. The course project will involve development of a regression model to fit a real data set. Lectures will be given primarily in matrix notation, i.e., using linear algebra. While the course will not be allencompassing in itself due to time constraints, it would be good preparation for more advanced modeling courses involving data mining, machine learning, "Big Data", and so on. Prior understanding of statistical concepts is assumed. Prerequisite:MTH115. MTH325. Knot Theory (Not offered 2014–15).
An introduction to the mathematical study of knots, including colorability, chirality, genus, and the Jones polynomial. Course will also explore the relationship between mathematical knots and structures in molecular chemistry and biology, and physics. Not open to students who have passedMTH225. Prerequisite:MTH221, MTH235, MTH332, orMTH340, or permission of the instructor.MTH330. Complex Analysis (Not offered 2014–15).
An introduction to analytic functions of a complex variable. Prerequisite: One200level course havingMTH199 as a prerequisite or permission of the instructor.MTH332. Abstract Algebra I (Spring).
Algebraic structures including groups, rings and fields. Prerequisite: One200level course havingMTH199 as a prerequisite or permission of the instructor.MTH336. Real Variable Theory (Fall).
A study of point sets on the real line and of real functions defined on these sets. Prerequisite:MTH332 orMTH340 or permission of the instructor.MTH340. Linear Algebra (Winter).
Vector spaces, linear transformations, inner product and dual spaces, eigenvalues and eigenvectors, special topics. Prerequisite:MTH115 and one200level course havingMTH199 as a prerequisite, or permission of the instructor.MTH432. Abstract Algebra II (Spring).
Continuation ofMTH332. Certain topics will be selected for more intensive study. Prerequisite:MTH332. MTH436. Topology (Not offered 2014–15).
Topological spaces, connectedness, compactness, continuous mappings and homeomorphisms. Prerequisite: One300level course or permission of the instructor.MTH448. Differential Geometry (Not offered 2014–15).
A study of curves and surfaces in3space. Topics include arc length, curvature, torsion, the Frenet trihedron, the first and second fundamental forms, normal curvature, and Gaussian curvature. Prerequisite: MTH117 andMTH340, or permission of the instructor.MTH480. Foundations of Mathematics (Same as Philosophy 480) (Not offered 2014–15).
Propositional and predicate logic, Gödel completeness theorem, introduction to recursion theory. Prerequisite:MTH332 or permission of the instructor.Independent Studies and Thesis
MTH295H–96H. TwoTerm Math Honors Independent Project 1 & 2
MTH490–96. Independent Study in Mathematics (Fall, Winter, Spring).
Independent study in a particular area of mathematics under the supervision of a faculty member.MTH497. OneTerm Senior Thesis (Fall, Winter)
MTH498–99. TwoTerm Senior Thesis (Fall–Winter)

