Common Curriculum 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 064) 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 2015–16).
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.
CC: QMRMTH053. Visualizing the Fourth Dimension (Fall).
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.
CC: QMRMTH054. Number Theory: From Clock Arithmetic to Unbreakable Codes (Spring).
An introduction to the beauty and use of numbers. Topics chosen from divisibility tests, prime numbers, perfect numbers, unbreakable codes, FermatÕs theorem, the golden section, calendars, magic squares,and others.
CC: QMRMTH055. Ancient Greek Mathematics (Not offered 2015–16).
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.
CC: QMRMTH056. History of Mathematics (Winter).
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. Topics include the interlinked changes and intercultural transmission of basic numeracy, arithmetic, geometry, trigonometry, algebra, practical computation and approximation, and concepts of the infinitely large and small.
CC: QMRMTH057. Game Theory and its Applications in the Humanities and Social Sciences (Not offered 2015–16).
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.
CC: QMR
Note: Not open to students who have passed MTH 199.MTH058. Applications of Mathematics to Economics I (Not offered 2015–16).
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.
CC: QMR
Note: Not open to students who have passed a college calculus course.MTH059. Applications of Mathematics to Economics II (Not offered 2015–16).
Differential and integral calculus with applications in the social sciences. Students who wish to continue the calculus after MTH 059 should enroll inMTH 112 .
Prerequisite(s): MTH 058.
CC: QMR
Note: Not open to students who have passed a college calculus course.MTH060. Mathematics and Politics (Not offered 2015–16) (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 PSC 112 would be relevant.
CC: QMRMTH061. Math in the Public Interest (Not offered 2015–16).
In what ways do advertisers, politicians, and other propagandists try to trick the public by exploiting our ignorance of or aversion to mathematical reasoning? This course 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.
CC: QMRMathematics 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.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 orMTH 059 .
CC: QMRMTH112. 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(s): MTH 110.
CC: QMRMTH113. AP Calculus (Fall).
Selfcontained treatment of the main topics in MTH 110 and MTH 112. Intended for firstyear students who have been introduced to (but have not yet mastered) the basics of differential and integral calculus.
CC: QMRMTH115. Calculus III: Differential Vector Calculus and Matrix Theory (Fall, Winter, Spring).
Geometry of 3space, differential calculus of functions of several variables, linear systems, matrices.
Prerequisite(s): MTH 102, MTH 112, or MTH 113.MTH117. Calculus IV: Integral Vector Calculus (Fall, Winter, Spring).
Double and triple integrals, line integrals and GreenÕs theorem, divergence and curl, divergence theorem and StokesÕ theorem.
Prerequisite(s): MTH 115.MTH127. Numerical Methods (Not offered 2015–16).
NewtonÕs method, numerical differentiation and integration, solution of ordinary differential equations, error estimates.
Prerequisite(s): MTH 115 and fluency in some mathematical programming language.MTH128. Probability (Winter) (Same as STA128.
Probability theory and applications.
Prerequisite(s): MTH 102, MTH 112, or MTH 113.MTH130. Ordinary Differential Equations (Winter, Spring).
Linear differential equations and power series.
Prerequisite(s): MTH 115.
Note: Not open to students who have passed MTH 234.MTH140. Applied Linear Algebra (Spring)
Linear algebra has an enormous number of applications to the sciences and engineering. This course will cover the basics of linear algebra in Euclidean nspace, including linear systems, linear transformations, determinants, eigenvalues and eigenvectors, orthogonality, and the singular value decomposition. An emphasis will be placed on applications, chosen from leastsquares fitting, linear programming, image compression, Markov chains and discrete dynamical systems, computer graphics, principal component analysis, the Google PageRank algorithm, and others. Computer software such as MATLAB or Mathematica will be used in this course to perform numerical calculations.
Prerequisite(s): MTH 115.
Credit will not normally be given for bothMTH 140 andMTH 340 . Exceptions require approval of a proposal from the student to the department chair.MTH197. Discrete Mathematics for Computer Science (Winter).
An introduction to fundamental concepts and methods of proof in mathematics and computer science. Topics include elementary logic, functions, relations, sets, and basic combinatorics. Not open to students who have passed MTH199.
CC: QMRMTH199. 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.MTH 115 is usually taken beforeMTH 199 . Credit is not normally given for both MTH197 and MTH199. Exceptions require the approval of the department chair.
Prerequisite(s): MTH 102, MTH 112, or MTH 113.MTH219. Topics in Discrete Mathematics (Fall).
Topics may include graph theory, partially ordered sets, algebraic coding theory, computational complexity, number theory.
Prerequisite(s): MTH 199 or permission from the Chair.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 passedMTH 235 orMTH 051 .
Prerequisite(s): MTH 199 or permission from the Chair.MTH224. Geometry (Spring).
Topics in transformation geometry, or projective, affine, Euclidean, and/or nonEuclidean geometries.
Prerequisite(s): MTH 199 or permission from the Chair.MTH234. Differential Equations (Winter).
Topics include systems of ordinary differential equation, series solutions, asymptotic solutions, integral equations.
Prerequisite(s): MTH 115 and MTH 199, or permission from the Chair.
Note: Not open to students who have passed MTH 130.MTH235. Number Theory (Not offered 2015–16).
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(s): MTH 199 or permission from the Chair.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(s):MTH 130 orMTH 234 andMTH 197 orMTH 199 .MTH325. Knot Theory (Fall).
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.
Prerequisite(s):MTH 221 ,MTH 235 ,MTH 332 , orMTH 340 , or permission of the Chair.
Note: Not open to students who have passed MTH225.MTH332. Abstract Algebra I (Spring).
Algebraic structures including groups, rings and fields.
Prerequisite(s): One ofMTH 219 ,MTH 221 ,MTH 224 ,MTH 235 or permission from the Chair.MTH336. Real Variable Theory (Fall).
A study of point sets on the real line and of real functions defined on these sets.
Prerequisite(s): MTH 332 or MTH 340 or permission from the Chair.MTH340. Linear Algebra (Winter).
Vector spaces, linear transformations, inner product and dual spaces, eigenvalues and eigenvectors, special topics.
Prerequisite(s): MTH 115 and one of MTH 219, MTH 221, MTH 224, MTH 235, or permission from the Chair.
Note: Credit will not normally be given for both MTH 140 and MTH 340. Exceptions require approval of a proposal from the student to the department chair.MTH430. Complex Analysis (Not offered 2015–16).
An introduction to analytic functions of a complex variable.
Prerequisite(s): One 300level course or permission from the Chair.MTH432. Abstract Algebra 2 (Not offered 2015–16).
Continuation of MTH 332 . Certain topics will be selected for more intensive study.
Prerequisite(s): MTH 332.MTH436. Topology (Not offered 2015–16).
Topological spaces, connectedness, compactness, continuous mappings and homeomorphisms.
Prerequisite(s): One 300level course or permission from the Chair.MTH448. Differential Geometry (Winter).
A study of curves and surfaces in 3space. Topics include arc length, curvature, torsion, the Frenet trihedron, the first and second fundamental forms, normal curvature, and Gaussian curvature.
Prerequisite(s): MTH 117 and MTH 340, or permission from the Chair.MTH480. Foundations of Mathematics (Spring) (Same as Philosophy 480).
Propositional and predicate logic, Godel completeness theorem, introduction to recursion theory.
Prerequisite(s): MTH 332 or permission from the Chair.
CC: HUMStatistics Courses
STA 064. Statistical Thinking (Not offered 2015–16) (Was MTH64)
Seeks to provide the conceptual foundation and analytical skills required to understand a complex, datarich and uncertain world, and to navigate through the daily bombardment of data from all sides. Significant emphasis is given to understanding the difficulties in acquiring highquality data, before moving on to graphical and statistical analysis of data, in order to draw actionable conclusions.
CC: QMR
Note: Not open to students who have passedSTA 104 ,ECO 243 ,MER 301 , orPSY 200 .STA104. Introduction to Statistics (Winter) (Was MTH104)
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 emphasized. This course is also intended to prepare students for more advanced statistics courses, such as those in experimental design or regression analysis.
CC: QMR
Note: Not open to students who have passedSTA 064 ,STA 264>/nobr>, MER 301 ,ECO 243 , orPSY 200 .STA128. Probability (Winter) (Same as MTH128)
Probability theory and applications
Prerequisite(s): MTH 102, MTH 112, or MTH 113STA164. Strategies of Experimentation: Statistical Design and Analysis of Experiments (Spring) (Was MTH164)
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.
Prerequisite(s): STA 104 (MTH 104) or STA 128 (MTH 128) or permission from the chair.STA264. Regression Analysis (Not offered 2015–16) (Was MTH264)
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, ÒBig DataÓ, and so on. Prior understanding of statistical concepts is assumed.
Prerequisite(s): MTH 115, STA 104 or permission from Chair.Independent Studies and Thesis
MTH295H–96H. TwoTerm Math Honors Independent Project 1 & 2
STA295H–96H. TwoTerm Statistics 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.STA490. Independent Study in Statistics (Fall, Winter, Spring).
MTH497. OneTerm Senior Thesis (Fall, Winter)
Independent study in a particular area of statistics under the supervision of a faculty member.
Note: Faculty permission required.MTH498–99. TwoTerm Senior Thesis (Fall–Winter)

