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Course Descriptions
MTRU/LU 1100, Finite Mathematics
Topics include solutions to systems of linear equations, counting techniques including Venn diagrams, permutations, combinations, probability, Bayes theorem, Markov chains.
MTRU/LU 1108, Mathematical Methods in Business I (open only to CBA students)
Topics include solutions to systems of linear equations, elementary matrix theory, linear programming, elementary counting techniques, probability, mathematics of finance.
MTRU/LU 1109, Mathematical Methods in Business II (open only to CBA students)
Topics include derivatives of polynomial, rational, exponential, and logarithmic functions, curve sketching, optimization problems, definite integrals, applications to business and economics.
MTRU/LU 1203, Applied Calculus I
This is an elementary course in calculus intended primarily for nonscience majors.
Derivatives of polynomial, rational, exponential, and logarithmic functions, curve sketching, optimization problems, definite integrals.
MTRU/LU 1204, Applied Calculus II
Topics include derivatives of trigonometric functions, methods of integration and applications, calculus of functions of several variables, Lagrange multipliers.
Prerequisite: MTRU/LU 1203 or equivalent.
MTRU/LU 1206, Calculus I
Functions, limits, continuity, Intermediate Value Theorem, derivatives and applications, antiderivatives, Riemann sums, definite integrals, the FundamentalTheorem of Calculus.
MTRU/LU 1207, Calculus II
Definite integrals, area, volume, work, techniques of integration, inverse functions, logarithmic and exponential functions, Taylor polynomials.
Prerequisite: MTRU/LU 1206 or equivalent.
MTRU/LU 1700, Mathematical Modeling
Building and using discrete and continuous mathematical models. Applications to mathematics, physical sciences, biology, economics. Computer explorations with software packages like Maple.
Prerequisite: MTRU/LU 1206 or equivalent.
MTRU 1750, Financial Engineering
The mathematics of portfolio management and derivative pricing. Various models of asset valuation will be discussed. Students will apply these models to a portfolio of assets.
Prerequisite: MTRU 1108 & 1109 or equivalents, and ECRU2142.
MTRU/LU 2001, Discrete Mathematics
Topics include elementary logic, set theory, basic counting techniques including generating functions, induction, recursion, recurrence.
Prerequisite: MTRU/LU 1206.
MTRU/LU 2004, Multivariable Calculus I
Topics include sequences and series, power series, uniform convergence, vector methods of solid geometry, vector-valued functions, functions of several variables, partial derivatives, gradients, Lagrange multipliers.
Prerequisite: MTRU/LU 1207.
MTRU/LU 2005, Multivariable Calculus II
Topics include the implicit function Theorem, vector fields and their derivatives, multiple integrals, line and surface integrals, Gauss, Green and Stokes Theorems.
Prerequisite: MTRU/LU 2004.
MTRU/LU 2006, Linear Algebra
Topics include systems of linear equations, real and complex vector spaces, linear independence, dimension, linear transformations, matrix representations, kernel and range, determinants and eigenvalues.
Prerequisites: MTRU/LU 1207 and MTRU/LU 2001.
MTRU/LU 3001, Linear Algebra II
Topics include vector spaces over arbitrary fields, Jordan canonical form, inner product spaces, coding theory.
Prerequisite: MTRU/LU 2006.
MTRU/LU 3002, Differential Equations
Topics include existence and uniqueness Theorems for ordinary differential equations, linear differential equations, power series solutions, and numerical methods.
Prerequisite: MTRU/LU 1207.
MTRU/LU 3003, Real Analysis
Topics include cardinality of sets, limits, continuity, uniform continuity, sequences and series of numbers and functions, modes of convergence, compact sets and associated Theorems.
Prerequisite: MTRU/LU 2005.
MTRU/LU 3004, Complex Analysis
Topics include complex numbers and mappings, analytic functions, Cauchy-Riemann equations, Cauchy integral Theorem, Taylor and Laurent series expansions, residue theory.
Prerequisite: MTRU/LU 2005.
MTRU/LU 3005, Abstract Algebra
Topics include well-ordering and induction, unique factorization, modular arithmetic, groups, subgroups, Lagrange's Theorem, normality, homomorphisms of groups, permutation groups, simple groups.
Prerequisite: MTRU/LU 2006.
MTRU/LU 3006, Probability
Topics include discrete and continuous probability models in one and several variables, expectation and variance, limit Theorems, applications.
Prerequisite: MTRU/LU 2005.
MTRU/LU 3007, Statistics
Topics include sampling distributions, estimation, testing hypotheses, analysis of variance, regression and correlation, nonparametric methods, time series.
Prerequisite: MTRU/LU 3006.
MTRU/LU 3008, Number Theory
Topics include divisibility and related concepts, congruencies, quadratic residues, number theoretic functions, addtive number theory, some Diophantine equations.
Prerequisite: MTRU/LU 2006.
MTRU/LU 3009, Mathematics of Finance
Review of time value of money and riskless assets, Portfolio Management and the Capital Asset Pricing Model, Introduction to Options and the Principle of No Arbitrage, Binomial Tree and other Discrete Time Pricing Models, Cox-Ross-Rubenstein Formula for Pricing Options.
Prerequisite: MTRU/LU 3006 .
MTRU/LU 4001, Operations Research
Topics include introduction to linear programming, statistical inference, decision theory, queuing theory, inventory theory, Markov chains.
Prerequisites: MTRU/LU 2006 and MTRU/LU 3002.
MTRU/LU 4002, Mathematical Structures
Topics include graphs, digraphs and trees, connectivity, searching, sorting, scheduling.
Prerequisite: MTRU/LU 2001.
MTRU/LU 4003, Abstract Algebra II
Topics include Sylow Theorems, solvable groups, field extensions, Galois theory, polynomial equations.
Prerequisite: MTRU/LU 3005.
MTRU/LU 4004, Topology
Topics include open sets and continuity in metric and topological spaces, subspaces and quotient topologies, compact sets, connected sets.
Prerequisites: MTRU/LU 2005 and permission of the instructor.
MTRU/LU 4006, Numerical Analysis
Topics include approximation of functions, interpolation, solutions to systems of equations, numerical integration, solutions to differential equations, error analysis.
Prerequisites: MTRU/LU 1600 and MTRU/LU 2006.
The department of mathematics also offers the following advanced courses upon request:
MTRU/LU 4007, Topics in Algebra
MTRU/LU 4008, Topics in Analysis
MTRU/LU 4009, Topics in Geometry
MTRU/LU 4010, Topics in Topology
MTRU/LU 4011, Topics in Applied Mathematics
MTRU/LU 4013, Problem Seminar
MTRU/LU 4999, Independent Study
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