# Mathematics/Actuarial Studies

## Required Courses (29 credits)

### MATN 121 - Calculus I (4 credits)

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.

### MATN 122 - Calculus II (4 credits)

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.

### MATN 201 - Advanced Calculus I (3 credits)

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.

### MATN 202 - Advanced Calculus II (3 credits)

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.

### MATN 231 - Probability Theory (3 credits)

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.

### MATN 232 - Quantitative Analysis (3 credits)

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.

### MATN 493 - Research Project in Mathematics (3 credits)

Prerequisite: Senior status or Departmental permission.

#### One of the following:

### MATN 211 - Linear Algebra (3 credits)

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.

### MATN 351 - Econometrics (3 credits)

Statistical techniques used to test the direction of economic variables or the relationship between economic variables; regression and correlation analysis; hypothesis testing and confidence intervals; time series analysis and forecasting. Prerequisites: EBEN 101 or EBEN 102 and either MATN 231 or MATN 261.

#### One of the following:

### MCON 141 - Introduction to Programming (3 credits)

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.

### EBFN 101 - Principles of Finance (3 credits)

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.

## Four electives From the Following (12 credits)

### MATN 240 - Finite Math (3 credits)

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.

### MATN 263 - Operations Research (3 credits)

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

### MATN 301 - Foundations of Analysis I (3 credits)

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.

### MATN 302 - Foundations of Analysis II (3 credits)

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.

### MATN 331 - Mathematics of Compound Interest (3 credits)

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.

### MATN 333 - Actuarial Mathematics I (3 credits)

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.

### MATN 334 - Actuarial Mathematics II (3 credits)

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.

### MATN 341 - Numerical Methods (3 credits)

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.

### MATN 405 - Methods of Applied Mathematics (4 credits)

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.

*Students can also take any 3 credit course approved by the Dept. Chair.*

## Recommended Business Courses

### EBAN 101 - Principles of Accounting I (3 credits)

Introduction to the double-entry system of debits and credits, journal entries and general ledger accounts, steps leading up to financial statement preparation and format of financial statements. Also included are studies of merchandising companies and determination of inventory balances and cost of goods sold, and an introduction to the accounting treatment of various assets and liabilities. US accounting standards (GAAP) are contrasted with international standards (IFRS).

### EBEN 101 - Principles of Macroeconomics (3 credits)

An introductory course covering issues relating to the economy as a whole. Topics covered include, but are not limited to, the study of national income and the Gross Domestic Product (GDP), national income determination, investment, consumption and consumption theories; classical economic theories, Keynesianism, monetarism, rational expectations, supply-side economics; the business cycle, inflation, unemployment; money and the money supply, the banking system, the federal reserve system, monetary and fiscal policy, budget deficits and the national debt.

### EBEN 102 - Principles of Microeconomics (3 credits)

An introductory course covering issues relating to individual economic units: namely, the individual consumer, the individual firm, the individual factors of production—land, labor, and capital. Topics covered include, but are not limited to, price theory, price determination through equilibrium, supply and demand, analysis of consumer demand, utility theory and marginal utility, consumer equilibrium, indifference curve analysis, analysis of supply, theory of production, pricing in perfectly and imperfectly competitive markets, types of imperfect competition, anti-trust laws in the U.S., and distribution of income.

### EBFN 220 - Corporate Finance (3 credits)

Methods of capital budgeting and corporate financial decision-making; valuation techniques, market efficiency, capital structure, dividend policy, Betas, cost of capital, portfolio analysis and the Miller Modigliani principle are incorporated into the analysis; financial analysis under conditions of certainty and uncertainty. Prerequisite: EBFN 101.

### EBFN 310 - Security Analysis (3 credits)

A continuation of Investment Principles (EBFN 210). Both fundamental and advanced approaches to valuation of securities and portfolios are developed. The risk/return trade-off and the selection of optimum portfolios are examined in depth, including reductionof-risk techniques. Prerequisite: EBFN 210.

### EBFN 210 - Investment Principles (3 credits)

Characteristics and investment strategies related to stocks, bonds, and options. Sources of return and risk are explored. The foundations of financial research are developed with regard to information sources, valuation techniques, computation of return and risk and their relationship. SEC regulations; methods of performance evaluation. Prerequisite: EBFN 101.

### EBFN 410 - Seminar in Options Trading (3 credits)

The theoretical foundations, institutional details, and practical applications of options trading: various pricing models and their development; in-depth examination of the use of options as speculative, hedging, investment, and arbitrage tools; the role of options with respect to the proper functioning of the modern market economy. The central focus is on stock options. Prerequisite: EBFN 210.