Mathematics Major Curriculum

Continuity, limits, differentiation, and integration of polynomial, exponential, and trigonometric functions. Curve sketching and related rates. Definite integrals, arc length, parametric equations and conic sections. Applications to geometry, physics, and other areas. Prerequisite: MATN 120 or placement by departmental examination.

Continuity, limits, differentiation, and integration of polynomial, exponential, and trigonometric functions. Curve sketching and related rates. Definite integrals, arc length, parametric equations and conic sections. Applications to geometry, physics, and other areas. Prerequisite: MATN 120 or placement by departmental examination.

Continuation of MATN 121-122. Functions of several variables and partial differentiation; directional derivative, gradient and Lagrange Multipliers; vector algebra and analysis; multiple integrals and Jacobians; infinite sequences and series; Taylor series; complex numbers, Euler’s formula and deMoivre’s formula; introduction to elementary theory of ordinary differential equations; separation of variables; linear equations with constant coefficients; and series solutions. Prerequisite: MATN 122.

Continuation of MATN 121-122. Functions of several variables and partial differentiation; directional derivative, gradient and Lagrange Multipliers; vector algebra and analysis; multiple integrals and Jacobians; infinite sequences and series; Taylor series; complex numbers, Euler’s formula and deMoivre’s formula; introduction to elementary theory of ordinary differential equations; separation of variables; linear equations with constant coefficients; and series solutions. Prerequisite: MATN 122.

Permutations and combinations, Classical and Modern theory, Discrete and continuous theory, Random variables, Probability Distribution Functions, Cumulative Distribution Functions, Binomial, Poisson, normal and other probability distributions, Conditional and marginal distributions, Expectation, mean, variance, Bayes Theorem, Approximations. Prerequisite: MATN 122.

Chi-square, t and F Distributions and Statistics, Moment generating functions of probability distributions, Multivariate distributions, Joint Statistics, Transformations of random variables, Sums of Random Variables, Convolution Integral, Min and Max Functions on Random Variables, Distributions of Order Statistics, Estimation Theory. Prerequisite: MATN 231.

Prerequisite: Senior status or Departmental permission.

Linear equations, matrices and determinants; linear transformations; vector spaces; eigenvalues and eigenvectors; similarity of matrices; canonical forms and invariant subspaces; LU decomposition. Matrix calculations on scientific calculators. Prerequisite: MATN 122.

A one-semester basic introduction to mathematical statistics and inference which will cover the learning objectives for Society of Actuaries Exam P. Topics include: concepts of random sampling, statistical inference and sampling distribution, methods of estimation and the main properties of estimators. Methods include matching moments, percentile matching, maximum likelihood, least squares. Properties studied include: bias, variance, mean squared error, consistency, efficiency, and UMVUE. Confidence intervals for unknown parameters, including the mean, differences of two means, variances, and proportions. Hypothesis testing including: Neyman-Pearson lemma, significance and power, likelihood ratio test, and information criteria. Testing for mean, variance, contingency tables, and goodness-of-fit. (This course is calculus-based) Prerequisite: MATN 231.

This course introduces students to problem solving techniques used in programming. In order to reinforce these concepts in a concrete manner, students will develop numerous programs using a popular programming language. They will implement programs using objects, input, output and variables and utilize programming control structures such as loops, selection structures, methods, and classes. Corequisite: MCON 104.

An introductory study of the basic principles, instruments, and institutions in the financial marketplace. Topics include the concept of money; the Federal Reserve and the banking system; the provision and management of funds for both the short and long terms; the basic financial instruments; financial characteristics of the firm, including basic balance sheet analysis; the role of the stock and bond markets; interest rates and present value analysis; personal finance issues. Corequisite: EBEN 101 or EBEN 102.

This course will give the student a basic knowledge of VBA programming in Excel with a view to developing financial models. The student will learn about VBA programming in relation to solving real-world problems. Applications of VBA and Excel to problems from Physics, Economics, and Biology will be presented. Mathematical Modeling techniques. Prerequisite: MATN 121 and MCO 140 or 104 or GCO 120.

Introduction to group theory, rings, and fields, with examples; polynomials, algebraic number fields, extension fields and applications. Introduction to solvability of polynomials and Galois theory. Prerequisite: MATN 122.

Review of set algebra, functions and relations; Boolean algebra and applications; counting techniques and elementary combinations; basic concepts of probability, theory of logic, vectors and matrices, linear systems of equations, Gauss Jordan, Cramer’s rule and matrix inverse methods; linear programming. Introduction to permutation groups and group theory. Prerequisite: MATN 120 or examination.

Techniques in operations research: deterministic and probabilistic models, applications employing linear programming, inventory models, queuing theory and game theory. Prerequisite: MATN 240.

This course will give the student a basic knowledge of VBA programming in Excel with a view to developing financial models. The student will learn about VBA programming in relation to solving real-world problems. Applications of VBA and Excel to problems from Physics, Economics, and Biology will be presented. Mathematical Modeling techniques. Prerequisite: MATN 121 and MCO 140 or 104 or GCO 120.

The real numbers system: limits, sequences, continuity, derivatives; Riemann and Stieltjes integral, infinite series, implicit function theorem, and vector integral theorems; introduction to point set topology, Lebesgue measure and integration; introduction to differential geometry and applications of analysis. Prerequisite: MATN 202 and Departmental permission.

The real numbers system: limits, sequences, continuity, derivatives; Riemann and Stieltjes integral, infinite series, implicit function theorem, and vector integral theorems; introduction to point set topology, Lebesgue measure and integration; introduction to differential geometry and applications of analysis. Prerequisite: MATN 202 and Departmental permission.

This course focuses on Differential Equations and Computational Methods. It is intended for Mathematics and Science students who are going to apply these techniques in their coursework. Reflecting the shift in emphasis from traditional methods to new computerbased methods, we focus on the mathematical modeling of real-world phenomena as the goal for the study of differential equations. Topics covered include standard methods for 1st order equations (separation of variables, integrating factor for linear equation, etc.), population models, equilibrium and stability, acceleration-velocity models, numerical methods, Euler, Improved Euler, Runge-Kutta, linear equations of higher order, resonance in mechanical and electrical systems, systems of ODEs eigenvalues and numerical methods; nonlinear systems with applications to population modeling and nonlinear mechanics, chaos, and Laplace transform techniques. Prerequisite or Corequisite: MATN 122.

Measurement of interest, simple and compound interest, present value, rate of discount, varying interest, time determination, equations of value; annuities, perpetuities, yield rates, time-weighted rates, portfolio methods and investment year methods; amortization schedules and sinking funds; bonds, securities and other financial instruments. Prerequisite: MATN 121. Corequisite: MATN 122.

Probability for Age at Death, Life Tables, Deterministic Survivorship Groups, Fractional Ages, Analytical laws of Mortality, Select Ultimate Tables, Insurance Payable at Moment of Death, Insurance Payable at End of the Year of Death, Recursion Equations, Contingent Life Annuities, Continuous Annuities, Discrete Annuities, Annuities with Monthly Payments, Varying Annuities, Complete and Apportionable Annuities, Continuous and Discrete Premiums, monthly Payment Premiums, Apportionable Premiums. Prerequisite: MATN 331.

Multiple life functions; probabilities and expectations, special mortality laws, simple contingent functions; multiple decrement models-two random variables, construction of multiple decrement tables; valuation theory for pension plans; insurance models including expenses; non-forfeiture benefits and dividends. Prerequisite: MATN 333.

I. Introduction to numerical methods; elementary discussion of error, approximation, interpolation; solutions of systems of linear equations, and linear and non-linear ordinary differential equations; II. Numerical integration and differentiation, matrix inversion, evaluation of determinants, and calculation of eigenvalues and eigenvectors, methods for solving partial differential equations. Prerequisite: MATN 202 and 141 or permission of instructor.

Introduction to computer algebra systems and scientific programming packages to solve real world problems: Maxima/Octave/Mathematica/Maple; data visualization, solving equations, differentiation, integration, matrices and vectors; Algorithms, sequences, selections, loops, functions, numeric and string types, arrays, vectors, simulations, visualization in 2D and 3D; Applications covered to be selected from this list depending upon student interest: least squares data fitting of Dow Jones index, projectile motion, Monte Carlo simulations, fractal patterns, electric field patterns, rigid body rotations, Black–Scholes financial equation; Vector and tensor analysis, special functions, Fourier and Laplace transforms, perturbation and variational methods, asymptotic expansions, and separation of variables. Prerequisite: MATN 202.