Mathematics Minor

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.

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.

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, 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.

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.

TBD

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, 156 construction of multiple decrement tables; valuation theory for pension plans; insurance models including expenses; non-forfeiture benefits and dividends. Prerequisite: MATN 333.

Introduction to numerical methods; elementary discussion of error, approximation, interpolation; solutions of systems of linear equations, and linear and non-linear ordinary differential equations.

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.

Introduction to computer algebra systems and scientific programming packages to solve real world problems: Maxima/Octave/Mathematica/Maple; data visualization, integration, solving matrices equations, differentiation, 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.