MATH 2030
ITERATIVE METHODS
3 units

TOPICS INCLUDE MATRIX THEORY, MATRIX AND VECTOR NORMS, ERROR ANALYSIS, FACTORIZATIONS, DIRECT AND ITERATIVE METHODS FOR SOLVING LINEAR SYSTEMS, LEAST SQUARES AND THE ALGEBRAIC EIGENVALUE PROBLEM.

MATH 2050
GRAPH THEORY
3 units

BASIC CONCEPTS AND DEFINITIONS FROM THE THEORY ARE STUDIED. IN PARTICULAR, ENUMERATIVE PROBLEMS ARE SELECTED BY THE INSTRUCTOR.

MATH 2060
COMBINATORICS
3 units

COURSE SURVEYS BASIC USES OF COMBINATORICS INCLUDING PERMUTATIONS AND COMBINATIONS. FURTHER TOPICS INCLUDE POLYA'S THEOREM AND OTHER ENUMERATIVE PROBLEMS AND CONSTRUCTIVE PROBLEMS SELECTED BY THE INSTRUCTOR.

MATH 2070
NUMERCL METH IN SCI COMPUTNG 1
4 units

THIS IS AN INTRODUCTORY SURVEY COURSE FOR NON-NUMERICAL ANALYSIS STUDENTS. IT COVERS THE UNDERLYING THEORY AND COMPUTATIONAL ASPECTS OF NUMERICAL LINEAR ALGEBRA. TOPICS INCLUDE DIRECTIONAL ITERATIVE METHODS, COMPUTATION OF EIGENVALUES AND EIGENVECTORS AND LEAST SQUARES PROBLEMS.

MATH 2071
NUMERCL METH IN SCI COMPUTNG 2
4 units

THIS COURSE IS A CONTINUATION OF 2070. TOPICS INCLUDE NUMERICAL SOLUTIONS OF PDE'S BY FINITE DIFFERENCES AND FINITE ELEMENT METHODS. ALSO NUMERICAL DIFFERENTIATION AND INTEGRATION ARE COVERED.

MATH 2090
NUMERICAL SOLUTN ORDNRY DE
3 units

THE TOPIC COVERED IS MODERN METHODS FOR SOLVING INITIAL VALUE PROBLEMS. THIS WILL INCLUDE THE BASIC THEORY AND SOFTWARE IMPLEMENTATIONS AND NUMERICAL EXPERIMENTS.

MATH 2219
DYNAMICAL SYSTEMS
3 units

THIS COURSE WILL INTRODUCE THE STUDENT TO NEW CONCEPTS FROM DYNAMICAL SYSTEMS. INVARIANT MANIFOLDS, NORMAL FORM; BIFURCATIONS AND CHAOS WILL BE DISCUSSED FROM THE GEOMETRIC POINT OF VIEW. SOME GLOBAL ANALYSIS WILL ALSO BE DESCRIBED. NUMERICAL TOOLS AND METHODS FOR ANALYZING LOCAL BIFURCATIONS WILL ALSO BE DISCUSSED. EMPHASIS WILL BE ON PRACTICAL APPLICATIONS OF THESE TECHNIQUES.

MATH 2301
ANALYSIS 1
3 units

THIS COURSE IS AN INTRODUCTION TO REAL ANALYSIS/MEASURE THEORY AND FUNCTIONAL ANALYSIS.

MATH 2302
ANALYSIS 2
3 units

THIS COURSE PRESENTS AN INTRODUCTION TO THE ANALYSIS OF HOLOMORPHIC FUNCTIONS FOLLOWED BY AN INTRODUCTION TO HARMONIC ANALYSIS. IT IS A NATURAL CONTINUATION OF MATH 2301 ANALYSIS 1.

MATH 2303
ANALYSIS 3
3 units

THIS COURSE PRESENTS AN INTRODUCTION TO THE ANALYSIS OF HOLOMORPHIC FUNCTIONS FOLLOWED BY AN INTRODUCTION TO HARMONIC ANALYSIS. IT IS A NATURAL CONTINUATION OF MATH 2301 ANALYSIS 1.

MATH 2304
ANALYSIS 4
3 units

ANALYSIS 4 IS A NEW COURSE THAT FOLLOWS ON FROM THE ANALYSIS 1, 2, 3; ESPECIALLY ANALYSIS 2. ITS FOCUS WILL BE COMPLEX AND HARMONIC ANALYSIS. WE WILL INTEGRATE THIS NEW MATERIAL WITH THE REAL, FUNCTIONAL, COMPLEX AND HARMONIC ANALYSIS OF THE PREVIOUS THREE COURSES.

MATH 2500
ALGEBRA 1
3 units

THE BASIC CONCEPTS AND RESULTS OF GROUP THEORY ARE DEVELOPED WITH AN EMPHASIS ON FINITE GROUPS. TOPICS INCLUDE: HOMOMORPHISM THEOREMS, ISOMORPHISM THEOREMS, SYLOW THEOREMS, PERMUTATION REPRESENTATIONS AND HALL'S CHARACTERIZATION OF SOLVABLE GROUPS.

MATH 2501
ALGEBRA 2
3 units

IN THIS COURSE THE FUNDAMENTAL PROPERTIES OF RINGS, FIELDS AND MODULES ARE STUDIED.

MATH 2601
ADVANCD SCIENTIFIC COMPUTING 1
3 units

THESE COURSES DEVELOP THE COMPUTATIONAL MATHEMATICS OF EVOLVING AREAS OF CURRENT SCIENTIFIC INTEREST.

MATH 2602
ADVANCD SCIENTIFIC COMPUTING 2
3 units

COURSE DEVELOPS THE COMPUTATIONAL MATHEMATICS OF EVOLVING AREAS OF CURRENT SCIENTIFIC INTEREST.

MATH 2603
ADVANCD SCIENTIFIC COMPUTING 3
3 units

THESE COURSES DEVELOP THE COMPUTATIONAL MATHEMATICS OF EVOLVING AREAS OF CURRENT SCIENTIFIC INTEREST.

MATH 2604
ADVANCD SCIENTIFIC COMPUTING 4
3 units

THESE COURSES DEVELOP THE COMPUTATIONAL MATHEMATICS OF EVOLVING AREAS OF CURRENT SCIENTIFIC INTEREST.

MATH 2700
TOPOLOGY 1
3 units

A FIRST COURSE IN TOPOLOGY, SOME OF THE TOPICS COVERED INCLUDE SEPARATION AXIOMS, BASES AND SUB-BASES, PRODUCT AND QUOTIENT TOPOLOGY, HOMEOMORPHISMS, COMPACTNESS, THE BAIRE CATEGORY THEOREM, THE LINDELOF PROPERTY, CONNECTEDNESS, TOPOLOGICAL SPACES AND COMPACTIFICATION.

MATH 2701
TOPOLOGY 2
3 units

THIS COURSE IS A CONTINUATION OF 2700. IN THIS COURSE THE BASIC CONCEPTS AND RESULTS IN ALGEBRAIC TOPOLOGY WILL BE COVERED, THIS INCLUDES BOTH HOMOTOPY AND HOMOLOGY THEORY. IN PARTICULAR THE CALCULATION OF THE FUNDAMENTAL GROUP AND HOMOLOGY GROUPS FROM CHAIN COMPLEXES WILL BE COVERED.

MATH 2800
DIFFERENTIAL GEOMETRY 1
3 units

THIS COURSE COVERS INTRODUCTORY TOPICS IN DIFFERENTIAL GEOMETRY. TOPICS INCLUDE TOPOLOGICAL MANIFOLDS, DIFFERENTIAL STRUCTURES, TANGENT AND TENSOR BUNDLES, VECTOR FIELDS AND DIFFERENTIAL EQUATIONS, INTEGRAL MANIFOLDS AND RIEMANNIAN STRUCTURES.

MATH 2801
DIFFERENTIAL GEOMETRY 2
3 units

THIS COURSE IS A CONTINUATION OF 2800 AND ITS GOAL IS TO DEVELOP ADVANCED CONCEPTS IN DIFFERENTIAL GEOMETRY. SOME TOPICS WHICH MIGHT BE COVERED INCLUDE RIEMANN SURFACES AND THE DIFFERENTIAL GEOMETRY OF R4 AND IN PARTICULAR THE RELEVANCE OF THESE TO QUANTUM SUPERSTRING THEORY.

MATH 2810
ALGEBRAIC GEOMETRY
3 units

THIS COURSE IS AN INTRODUCTION TO THE BASIC IDEAS OF ALGEBRAIC GEOMETRY. THE APPROACH TO THE SUBJECT MAY BE VIA EITHER THE LINEAR SERIES ON A CURVE APPROACH OR THE ALGEBRAIC APPROACH THROUGH FIELDS OF ALGEBRAIC FUNCTIONS OR THE SHEAF THEORETIC APPROACH. APPLICATIONS MAY ALSO BE INCLUDED.

MATH 2900
PARTIAL DIFFERNTL EQUATIONS 1
3 units

THIS IS AN INTRODUCTION COURSE TO THIS AREA. SOME OF THE TOPICS TO BE COVERED INCLUDE: LINEAR SECOND ORDER EQUATIONS, THE METHOD OF CHARACTERISTICS, LAPLACE AND WAVE EQUATIONS, THE HEAT EQUATION AND VARIOUS MAXIMUM PRINCIPLES.

MATH 2901
PARTIAL DIFFERNTL EQUATIONS 2
3 units

THIS COURSE IS A CONTINUATION OF 2900. THE TOPICS COVERED IN THIS COURSE INCLUDE AN INTRODUCTION TO PARABOLIC AND HYPERBOLIC EQUATIONS, A PRIORI ESTIMATES, FREE BOUNDARY PROBLEMS, SHOCK WAVES AND RIEMANN PROBLEMS.

MATH 2920
ORDINARY DIFFERNTL EQUATNS 1
3 units

THIS COURSE COVERS BASIC CONCEPTS IN O.D.E.'S. IN PARTICULAR, EMPHASIS IS GIVEN TO CONNECTIONS OF THIS AREA TO APPLIED MATHEMATICS AND DIFFERENTIAL GEOMETRY

MATH 2921
ORDINARY DIFFERNTL EQUATNS
3 units

THIS COURSE IS A CONTINUATION OF 2920. SOME OF THE TOPICS WHICH ARE COVERED INCLUDE BOUNDARY VALUE PROBLEMS, GREEN'S FUNCTIONS, INTEGRAL EQUATIONS AND THE SPECTRAL THEORY OF SECOND ORDER DIFFERENTIAL EQUATIONS.

MATH 2930
ASYMPTOTICS & SPECIAL FUNCTNS
3 units

THIS COURSE IS AN INTRODUCTION TO THE THEORY OF ASYMPTOTICS AND SPECIAL FUNCTIONS. SOME OF THE FUNCTIONS STUDIED ARE THE GAMMA FUNCTION, ORTHOGONAL POLYNOMIALS AND BESSEL FUNCTIONS. THIS COURSE ALSO COVERS TECHNIQUES FOR FINDING ASYMPTOTIC EXPANSIONS OF INTEGRALS AND OF SOLUTIONS TO DIFFERENTIAL EQUATIONS.

MATH 2950
METHODS IN APPLIED MATHEMATICS
3 units

THIS COURSE IS A RIGOROUS TREATMENT OF VARIOUS ASPECTS OF NUMERICAL LINEAR ALGEBRA, SPECIAL FEATURES OF SYMMETRIC OPERATORS, OPTIMIZATION WITH EMPHASIS ON PROPERTIES OF CONVEX FUNCTIONS AND DUALITY THEORY.

MATH 3020
CALCULUS OF VARIATIONS
3 units

THIS COURSE IS AN INTRODUCTION TO THE SUBJECT. TOPICS INCLUDE: VARIATIONAL FORMULATION, THE EULER-LAGRANGE EQUATIONS, AND APPLICATIONS.

MATH 3071
NUMRC SOLUTN PARTL DIFFT EQUA
3 units

THIS COURSE COVERS CONTEMPORARY METHODS FOR SOLVING INITIAL AND BOUNDARY VALUE PROBLEMS. TOPICS INCLUDE: PROPERLY POSED PROBLEMS, CHARACTERISTICS, FINITE DIFFERENCE AND FINITE ELEMENT METHODS AND ERROR ESTIMATES.

MATH 3072
FINITE ELEMENT METHOD
3 units

TOPICS INCLUDE A DESCRIPTION OF THE METHOD IN ONE, TWO AND THREE DIMENSIONS, VARIATIONAL AND MINIMUM ENERGY PRINCIPLES, IMPLEMENTATION AND DISCUSSION OF THE NECESSARY DATA STRUCTURE AND EVALUATION OF THE ERRORS. POSSIBLY A SPECIAL TOPIC SUCH AS APPLICATIONS TO FLUID DYNAMICS WILL BE DONE.

MATH 3225
MATHEMATICS OF FINANCE 1
3 units

A MATHEMATICAL INTRODUCTION TO THE PRICING OF OPTIONS AND OTHER DERIVATIVE SECURITIES, PORTFOLIO THEORY AND RISK MANAGEMENT.

MATH 3226
MATHEMATICS OF FINANCE 2
3 units

THIS COURSE WILL INVESTIGATE THE MATHEMATICAL MODELING, THEORY AND COMPUTATIONAL METHODS IN MODERN FINANCE. IT WILL TREAT MATHEMATICAL MODELS FOR FINANCIAL RISK FACTORS, PRICING OF OPTIONS AND OTHER DERIVATIVE SECURITIES, BASIC PORTFOLIO THEORY AND ELEMENTARY RISK MANAGEMENT.

MATH 3227
MATH FINANCE 3
3 units

THIS COURSE COVERS SPECIAL TOPICS IN MATHEMATICAL FINANCE. TOPICS WILL INCLUDE: EXTENSIONS OF THE BLACK-SCHOLES MODEL TO ALTERNATIVE STOCHASTIC PROCESSES, RISK MANAGEMENT, MODELS FOR CREDIT RISK AND CREDIT DERIVATIVES, AMERICAN OPTIONS, PORTFOLIO SELECTION AND DERIVATIVES PRICING UNDER TRANSACTIONS COSTS.

MATH 3228
MATHEMATICS OF FINANCE 4
3 units

THIS COURSE COVERS ADVANCED TOPICS IN MODERN MATHEMATICAL FINANCE. TOPICS WILL INCLUDE: ADVANCED CREDIT RISK AND INTEREST RATE MODELS, STOCHASTIC CONTROL AND STOCHASTIC OPTIMIZATION MODELS FOR PORTFOLIO SELECTION AND OPTION PRICING, AND NUMERICAL METHODS.

MATH 3370
MATHEMATICAL NEUROSCIENCE
3 units

COURSE COVERS COMPUTATIONAL AND MATHEMATICAL NEUROSCIENCE. IT WILL DO MODELING AND ANALYSIS OF COMPLEX DYNAMICS OF SINGLE NEURONS AND LARGE-SCALE NETWORKS.

MATH 3375
CMPTL NEUROSCIENCE METHODS
3 units

HIS COURSE OFFERS AN INTRODUCTION TO MODELING METHODS IN NEUROSCIENCE. TOPICS RANGE FROM MODELING THE FIRING PATTERNS OF SINGLE NEURONS TO USING COMPUTATIONAL METHODS TO UNDERSTAND NEURAL CODING. SOME SYSTEMS LEVEL MODELING IS ALSO DONE

MATH 3380
MATHEMATICAL BIOLOGY
3 units

THIS COURSE INTRODUCES A NUMBER OF MODELING METHODS FOR BIOLOGICAL SYSTEMS. WE WILL EXAMINE A NUMBER OF PROBLEMS FROM CELL BIOLOGY, IMMUNOLOGY, POPULATION BIOLOGY, PHYSIOLOGY AND MOLECULAR GENETICS. THE MAIN TOOLS WILL BE TECHNIQUES FROM ORDINARY AND PARTIAL DIFFERENTIAL EQUATIONS. DISCRETE AND DELAY-DIFFERENTIAL EQUATIONS WILL ALSO BE USED. HOWEVER THE BACKGROUND FOR THESE WILL NOT BE ASSUMED. WE WILL TAKE MODELS FROM CURRENT AND CLASSIC PAPERS IN THE FIELD.