MATH 100. Intermediate Algebra

Required text(s):  Angel and Runde, Intermediate Algebra for College Students (packaged with MyMathLab):, Pearson-Prentice Hall (2011). ISBN-10: 0321709047, ISBN-13: 9780321709042. 8th Edition.

Textbook notes:  Alternatively, a student may purchase only MyMathLab since an online version of the entire textbook is included. Make sure any online purchase includes MyMathLab. The ISBN number given may not include MML if you order this book online.

Additional notes:  TI-84 Plus graphing calculator or equivalent is strongly recommended.

Prerequisites:  None

Course description:  Catalog Description: Fundamentals of algebra. Graphs of linear equations, polynomials and factoring, first and second-degree equations and inequalities, radicals and exponents, and systems of equations. Word problems emphasized throughout the course.

Syllabus:  Chapter 1: Basic Concepts (1.5 weeks) Real numbers Order of operations Exponents Scientific notation Chapter 2: Equations and Inequalities (2.5 weeks) Solving linear equations Story problems including (rate)(time)=distance and mixture problems Solving linear inequalities Solving equations and inequalities containing absolute values Chapter 3: Graphs and Functions (2.5weeks) Graphs, Functions Linear Functions, Graphs and story problems Slope-intercept form of a linear equation Point-slope form of a linear equation Algebra of functions Chapter 4: Systems of Equations and Inequalities (1 week) Solving systems of linear equations in two variables by substitution and by elimination Story problems Chapter 5: Polynomials and Polynomial and Functions (3 weeks) Addition, subtraction and multiplication of polynomials Division of polynomials (not including synthetic division) Remainder theorem Factoring methods (as time permits) Chapter 6: Rational Expressions and Equations (1.5 weeks) Domains, addition, subtraction, multiplication and division of rational expressions Work and rate story problems Chapter 7: Radicals and Complex Numbers (2 weeks) Roots and radicals, rational exponents Simplifying radicals Adding, subtracting and multiplying radicals (as time permits) Rationalizing denominators

  

MATH 108. Real World Modeling

Required text(s):  Consortium for Mathematics and Its Applications (COMAP, edited by S. Garfunkel) For All Practical Purposes: Mathematical Literacy in Today's World, 9th edition, W. H. Freeman (2011), ISBN: 978-1429-25482-3

Additional notes:  The instructor may choose from the following topics: 1. Management Science (Street Networks, Visiting Vertices, Planning and Scheduling, Linear Programming) 2. Coding Information (Identification Numbers, Transmitting Information) 3. Social Choice and Decision Making (Social Choice: The Impossible Dream, Weighted Voting Systems, Fair Division, Apportionment, Game Theory: The Mathematics of Competition) 4. On Size and Shape (Growth and Form, Symmetry and Patterns, Tilings), Modeling in Mathematics (Logic and Modeling, Consumer Finance Models)

Prerequisites:  None

Course description:  An introduction to mathematical modeling. Topics chosen from linear programming, probability theory, Markov chains, scheduling problems, coding theory, social choice, voting theory, geometric concepts, game theory, graph theory, combinatorics, networks. Emphasis placed upon demonstrating the usefulness of mathematical models in other disciplines, especially the social science and business.

Syllabus:  Possible Syllabus (syllabus varies): PART I - MANAGEMENT SCIENCE Chapter 1 - Street Networks [0.5 week] Euler Circuits, Finding Euler Circuits, Circuits with Reused Edges Chapter 2 - Visiting Vertices [1 week] Hamiltonian Circuits, Fundamental Principle of Counting, Traveling Salesman Problem, Strategies for Solving the Traveling Salesman Problem, Nearest-Neighbor Algorithm, Sorted-Edges Algorithm, Minimum-Cost Spanning Trees, Kruskal's Algorithm Chapter 3 - Planning and Scheduling [1 week] Scheduling Tasks, Assumptions and Goals, List-Processing Algorithm, When is a Schedule Optimal?, Strange Happenings, Critical-Path Schedules, Independent Tasks, Decreasing-Time Lists Chapter 4 - Linear Programming [1 week] Mixture Problems, Mixture Problems Having One Resource, One Product and One Resource: Making Skateboards, Common Features of Mixture Problems, Two Products and One Resource: Skateboards and Dolls, Mixture Charts, Resource Constraints, Graphing the Constraints to Form the Feasible Region, Finding the Optimal Production Policy, General Shape of Feasible Regions, The Role of the Profit Formula: Skateboards and Dolls, Setting Minimum Quantities for Products: Skateboards and Dolls, Drawing a Feasible Region When There are Nonzero Minimum Constraints, Finding Corner Points of a Feasible Region Having Nonzero Minimums, Evaluating the Profit Formula at the Corners of a Feasible Region with Nonzero Minimums, Summary of the Pictorial Method, Mixture Problems Having Two Resources, Two Products and Two Resources: Skateboards and Dolls, The Corner Point Principle, Linear Programming: The Wider Picture, Characteristics of Linear Programming Algorithms, The Simplex Method, An Alternative to the Simplex Method PART III - CODING INFORMATION Chapter 9 - Coding Information [1 week] The Zip Code, Bar Codes, Zip Code Bar Code, the UPC Bar Code Chapter 10 - Transmitting Information [1.5 weeks] Binary Codes, Encoding with Parity-Check Sums, Data Compression, Cryptography. PART IV - SOCIAL CHOICE and DECISION MAKING Chapter 12 - Social Choice: The Impossible Dream [1.5 weeks] Elections with Only Two Alternatives, Elections with Three or More Alternatives: Procedures and Problems, Plurality Voting and the Condorcet Winner Criterion, The Borda Count and Independence of Irrelevant Alternatives, Sequential Pairwise Voting and the Pareto Condition, the Hare System and Monotonicity, Insurmountable Difficulties: From Paradox to Impossibility, The Voting Paradox of Condorcet, Impossibility, A Better Approach? Approval Voting Chapter 13 - Weighted Voting Systems [2 weeks] How Weighted Voting Works, Notation for Weighted Voting, The Banzhaf Power Index, How to Count Combinations, Equivalent Voting Systems, The Shapley-Shubik Power Index, How to Compute the Shapley-Shubik Power Index, Comparing the Banzhaf and Shapley-Shubik Models Chapter 14 - Fair Division [1.5 weeks] The Adjusted Winner Procedure, The Knaster Inheritance Procedure, Divide-and-Choose, Cake-Division Procedures: Proportionality, Cake-Division Procedures: The Problem of Envy Chapter 15 - Apportionment [1.5 weeks] The Apportionment Problem, The Hamilton Method, Paradoxes of the Hamilton Method, Divisor Methods, The Jefferson Method, Critical Divisors, The Webster Method, The Hill-Huntington Method, Which Divisor Method is the Best? Chapter 16 - Game Theory: The Mathematics of Competition [as time permits] Two-Person Total-Conflict Games: Pure Strategies, Two-Person Total-Conflict Games: Mixed Strategies, A Flawed Approach, A Better Idea, Partial-Conflict Games, Larger Games, Using Game Theory, Solving Games, Practical Applications.

  

MATH 117. College Algebra

Instructor(s):  See Course Page

Required text(s):  Sheldon Axler, Algebra and Trigonometry with Wiley-Plus, 1st edition, Wiley, (2012), ISBN: 978-1118-08841-8.

Textbook notes:  Alternatively, a student may purchase only Wiley-plus since an online version of the entire book is included.

Additional notes:  TI-84 Plus graphing calculator or equivalent is strongly recommended.

Prerequisites:  Math 100 (Intermediate Algebra) with a grade of "C-" or better, or Math Placement Test

Course description:  Inverse functions, quadratic functions, complex numbers. Detailed study of polynomial functions including zeros, factor theorem, and graphs. Rational functions, exponential and logarithmic functions and their applications. Systems of equations, inequalities, partial fractions, linear programming, sequences and series. Word problems are emphasized throughout the course.

Syllabus:  Chapter 2 - Combining Algebra and Geometry [1.5 Weeks] 2.1 - (Cover very quickly.) The coordinate plane: coordinates, graphs of equations, distance formula, length, perimeter, circumference. 2.2 – (Cover very quickly.) Lines: slope, equation of a line, parallel/perpendicular lines, midpoints. 2.3 – Quadratic Expressions and Conic Sections: completing the square, quadratic formula, circles, ellipses, hyperbolas. Foci for ellipses/hyperbolas optional. 2.4 – (Cover very quickly.) Area: squares, rectangles, parallelograms, triangles, trapezoids, stretching, circles and ellipses. Chapter 3 – Functions and their Graphs [2.5 Weeks] 3.1 – Functions: definition, graphs, domain, range, tables. 3.2 – Function transformations and graphs: vertical/horizontal shifts, stretches, flips, combinations of transformations, even/odd functions. 3.3 – Composition of Functions: definition, importance of order, decomposing functions, composing 3 or more functions, transformations as functions. 3.4 – Inverse Functions: definition, one-to-one functions, domain/range of inverse functions, composition of a function and its inverse, importance of notation. 3.5 – A graphical approach to inverse functions: graph of inverse functions, horizontal line test, increasing/decreasing function, inverses via tables. Chapter 4 – Polynomial and Rational Functions [2.5 Weeks] 4.1 – Integer exponents: positive integer exponents, properties of exponents, negative integer exponents. 4.2 – Polynomials: degree, algebra of polynomials, zeros, factorization, behavior as x approaches positive/negative infinity, graphs. 4.3 – Rational functions: definition, algebra of rational functions, polynomial division, behavior as x approaches positive/negative infinity, graphs. 4.4 – Complex numbers: complex number system, arithmetic/algebra of complex numbers, conjugates, division, relation to zeros and factorization. Chapter 5 – Exponents and Logarithms [3 Weeks] 5.1 – Exponents and exponential functions: roots, rational exponents, real exponents, exponential functions. 5.2 – Logarithms as inverses of exponential functions: logarithms with arbitrary base, common logarithms, number of digits, logarithm of a power, decay/half-life problems. 5.3 – Applications of Logarithms: logarithm of products/quotients, change of base, richter scale, decibels. Apparent magnitude and sound intensity optional. 5.4 – Exponential growth: functions with exponential growth, population growth, compound interest. Chapter 6 – e and the Natural Logarithm [2 Weeks] 6.1 – Defining e and ln: estimating area using rectangles, definitions of e and ln, properties of ln. 6.2 (Optional) – Approximations of e and ln, and an area formula. 6.3 – Exponential growth revisited: continuous compounding of interest, continuous growth rates, doubling time. Chapter 7 – Systems of Equations [1 Week] 7.1 – Equations and systems of equations: solving an equation, solving a system graphically, solving a system by substitution. 7.2 – Solving systems of linear equations: linear equations and number of solutions, systems of linear equations, Gaussian elimination.

  

MATH 118. Precalculus

Required text(s):  Sheldon Axler, Algebra and Trigonometry with Wiley-Plus, 1st edition, Wiley, (2012), ISBN: 978-1118-08841-8

Textbook notes:  Alternatively, a student may purchase only Wiley-plus since an online version of the entire book is included.

Additional notes:  TI-84 Plus graphing calculator or equivalent is strongly recommended

Prerequisites:  Math 117 (College Algebra) with a grade of "C-" or better, or Math Placement Test

Course description:  Functions and change with an emphasis on linear, quadratic, exponential, and logarithmic functions and their graphs. Specific geometric topics include concavity and how transformations affect graphs. Topics in trigonometry include radians, sinusoidal functions, identities, sum/difference formulas, double/half angle formulas, and trigonometric equations. Other topics include polar coordinates

Syllabus:  Review of Prerequisite Material [1.5 Weeks] Quick review of algebra, lines, circles, quadratic expressions, functions followed by a more comprehensive review of the definitions and properties of exponential functions and logarithms. Exponential growth modeling can be covered lightly. Chapter 7 [Fall 2012 Only] – Systems of Equations [1 Week] 7.1 – Equations and systems of equations: solving an equation, solving a system graphically, solving a system by substitution. 7.2 – Solving systems of linear equations: linear equations and number of solutions, systems of linear equations, Gaussian elimination. Chapter 8 – Sequences, Series, and Limits [2 Weeks] 8.1 – Sequences: definition of sequence, arithmetic/geometric sequences, recursively defined sequences. 8.2 – Series: sums of sequences, definition of series, arithmetic/geometric series. Emphasize: summation notation. Binomial theorem is optional. 8.3 – Limits: introduction to limits, infinite series, decimals as series, special series. Chapter 9 – Trigonometric Functions [3 Weeks] 9.1 – The unit circle: equation of unit circle, angles, negative angles, angles greater than 360 degrees, arc length, special points on unit circle. 9.2 – Radians: motivation of radians, radius corresponding to an angle, arc length revisited, area of slices, special points on unit circle revisited. 9.3 – Cosine and sine: definition of cosine and sine, signs of cosine and sine, pythagorean identity, graphs of cosine and sine. 9.4 – More trigonometric functions: tangent, sign of tangent, connections between cosine, sine, and tangent, graph of tangent, definitions of cotangent, secant, cosecant. 9.5 – Trigonometry in right triangles: definition of trigonometric functions via right triangles, two sides of a right triangle, one side and one angle of a right triangle 9.6 – Trigonometric identities: relationship between cosine, sine, tangent, identities for negative angles, identities involving pi/2, identities involving multiples of pi Chapter 10 – Trigonometric Algebra and Geometry [3 Weeks] 10.1 – Inverse trigonometric functions: arccosine, arcsine, and arctangent functions. 10.2 (Optional) – Inverse trigonometric identities, graphical and algebraic approach to evaluation at -t 10.3 – Using trigonometry to compute area: area of triangle/parallelogram via trigonometry, ambiguous angles, areas of polygons, trigonometric approximations. 10.4 – Law of Sines and Law of Cosines: statement and uses of laws of sines/cosines, when to use which law. 10.5 – Double-Angle and Half-Angle Formulas: sine/cosine double-angle and half-angle formulas. The corresponding formulas for tangent are optional. 10.6 – Addition and subtraction formulas: sine/cosine/ sum and difference formulas. The corresponding formulas for tangent are optional. Chapter 11 – Applications of Trigonometry [2.5 Weeks] Suggestion: If time is short, 11.1 is optional. Focus on 11.2, 11.3, and 11.5. Suggestion: Quickly review Chapter 3, Section 2 before covering 11.2 11.1 (Optional) – Parametric curves: curves in the plane, inverse functions as parametric curves, shifts/flips of parametric curves. Stretches of parametric curves is optional. 11.2 – Transformations of trigonometric functions: amplitude, period, phase shift, modeling periodic phenomena, modeling with data. 11.3 Polar Coordinates: Definition of polar coordinates, conversion between polar/rectangular coordinates, graphs of circles and rays. Other polar graphs are optional. 11.4 (Optional) – Algebraic and geometric introduction to vectors, addition and subtraction, scalar multiplication, dot product. 11.5 – The complex plane: complex numbers as points in the plane, geometric interpretation of multiplication/division of complex numbers, De Moivre's theorem, finding complex roots.

  

MATH 131. Applied Calculus I

Required text(s):  D. Hughes-Hallett, A. Gleason, et al, Applied Calculus with WileyPlus, 4th edition, Wiley (2009), ISBN 978-0-47-057877-3

Textbook notes:  Alternatively, a student may purchase only WileyPlus since an online version of the entire textbook is included. Make sure any online purchase includes WileyPlus. The ISBN number given may not include WileyPlus if you order this book online.

Additional notes:  TI-84 Plus graphing calculator or equivalent is strongly recommended

Prerequisites:  Math 118 (Precalculus) with a grade of "C-" or better, or appropriate score on the Math Diagnostic Test

Course description:  An introduction to differential and integral calculus, with an emphasis on applications. This course is intended for students in the life and social sciences, computer science, and business. Topics include: modeling change using functions including exponential and trigonometric functions, the concept of the derivative, computing the derivative, applications of the derivative to business and life, social, and computer sciences, and an introduction to integration. This course is not a substitute for Math 161

Syllabus:  13 weeks Chapter 1: Review of Functions [2 weeks] Chapter 2: Rate of change- the derivative [2 weeks] Chapter 3: Rules for derivatives [2 weeks] Chapter 4: Applications- Optimization, graphing, business [3 weeks] Chapter 5: The definite integral [2 weeks] Testing and Review [2 weeks]

  

MATH 132. Applied Calculus II

Required text(s):  D. Hughes-Hallett, A. Gleason, et al, Applied Calculus with WileyPlus, 4th edition, Wiley (2009), ISBN 9780470578773

Textbook notes:  Alternatively, a student may purchase only WileyPlus since an online version of the entire textbook is included. Make sure any online purchase includes WileyPlus. The ISBN number given may not include WileyPlus if you order this book online

Additional notes:  TI-84 Plus graphing calculator or equivalent is strongly recommended

Prerequisites:  Math 131 (Applied Calculus I) with a grade of "C-" or better, or Math Diagnostic Test

Course description:  A continuation of Math 131. Topics include: properties of the integral, techniques of integration, numerical methods, improper integrals, applications to geometry, physics, economics, and probability theory, introduction to differential equations and mathematical modeling, systems of differential equations, power series. This course is not a substitute for Math 162

Syllabus:  13 weeks Chapter 5: The definite integral [1 week] Chapter 6: The definite integral and applications [2 weeks] Chapter 7: Antiderivatives [2 weeks] Chapter 8: Probability [1 week] Chapter 9: Functions of several variables [2.5 weeks] Chapter 10: Modeling and differential equations [2.5 weeks] Testing and Review 2 weeks

  

MATH 161. Calculus I

Required text(s):  George Thomas, et. al., Calculus Early Transcendentals (Part 1), 12th edition, Addison Wesley (2009), packaged with MyMathLab Access Kit. ISBN Volume 1 ET + MML: 0-321-705408

Textbook notes:  Alternatively, a student may purchase MyMathLab as a separate entity and use the online version of the book. Make sure any online purchase includes MML

Additional notes:  The instructor may require the use of Mathematica in this course

Prerequisites:  Math 118 (Precalculus) with a grade of "C-" or better, or Math Placement Test

Course description:  A traditional introduction to differential and integral calculus. Functions, limits, continuity, differentiation, intermediate and mean-value theorems, curve sketching, optimization problems, related rates, definite and indefinite integrals, fundamental theorem of calculus, logarithmic and exponential functions. Applications to physics and other disciplines

Syllabus:  Chapter 1 - Functions [1 week] Functions and Their Graphs, Identifying Functions. Mathematical Models. Combining Functions: Shifting and Scaling Graphs. Graphing with Calculators and Computers (Introduction to Mathematica). Exponential Functions. Inverse Functions and Logarithms. Optional: Hyperbolic functions. Chapter 2 - Limits and Continuity [1.5 weeks] Rates of Change and Limits. Calculating Limits Using the Limit Laws. The Precise Definition of a Limit. One-Sided Limits and Limits at Infinity. Infinite Limits and Vertical Asymptotes. Tangents and Derivatives Chapter 3 - Differentiation [4 weeks] The Derivative as a Function. Differentiation Rules: for Polynomials and Exponentials, Products, and Quotients. The Derivative as a Rate of Change. Derivatives of Trigonometric Functions. The Chain Rule and Parametric Equations. Implicit Differentiation. Derivatives of Inverse Functions and Logarithms. Inverse Trigonometric Functions. Related Rates. Linearization and Differentials. Derivatives of Hyperbolic Functions. Chapter 4 - Applications of Derivatives [3 weeks] Extreme Values of Functions. Rolle’s Theorem and the Mean Value Theorem. Monotonic Functions and the First Derivative Test. Concavity and Curve Sketching. Applied Optimization Problems. Indeterminate Forms and L’Hopital’s Rule. Newton’s Method. Antiderivatives. Chapter 5 - Integration [4 weeks] Estimating with Finite Sums. Sigma Notation and Limits of Finite Sums. The Definite Integral. The Fundamental Theorem of Calculus. Indefinite Integrals and the Substitution Rule. Substitution and Area between Curves.

  

MATH 162. Calculus II

Required text(s):  George Thomas, et. al., Calculus Early Transcendentals. (Part 1), 12th edition, Addison Wesley (2010), packaged with MyMathLab Access Kit. ISBN Volume 1 ET + MML: 0-321-705408

Textbook notes:  Alternatively, a student may purchase MyMathLab as a separate entity and use the online version of the book. Make sure any online purchase includes MML

Additional notes:  The instructor may require the use of Mathematica in this course

Prerequisites:  Math 161 (Calculus I) with a grade of "C-" or better or departmental permission

Course description:  A continuation of Math 161. Calculus of logarithmic, exponential, inverse trigonometric, and hyperbolic functions. Techniques of integration. Applications of integration to volume, surface area, arc length, center of mass, and work. Numerical sequences and series. Study of power series and the theory of convergence. Taylor's theorem with remainder

Syllabus:  REVIEW (particularly of Chapter 5) – Integration [1 week] Rapid review of areas and distances and the Definite Integral and The Fundamental Theorem of Calculus. Chapter 6 – Applications of Definite Integrals [2-3 weeks] Using integrals to calculate volumes of solids, length of curves, surface areas of solids of revolution, and applications to physics (instructor to select from moments and center of mass, work, fluid pressures and forces). Chapter 7 – Integrals of Transcendental Functions [1 week] The logarithm defined as an integral, exponential functions, and hyperbolic functions. Chapter 8 – Techniques of Integration [3 weeks] Basic integration formulas, integration by parts, integration of rational functions by partial fractions, trigonometric integrals, trigonometric substitution, integration using tables and computer algebra systems, approximate integration. Improper integrals of Type I and Type II; comparison tests for convergence of improper integrals. Chapter 10 – Infinite Sequences and Series [4 weeks] Numerical sequences, series, integral test and estimates of sums, comparison tests, alternating series, conditional convergence, absolute convergence, alternating series, the ratio and root tests, strategy for testing convergence of series, the rearrangement theorem for absolutely convergent series. Power series, representations of functions as power series, Taylor and Maclaurin series, binomial series, applications of Taylor polynomials. Complex numbers and Euler's identity. Chapter 11 – Conic Sections and Polar Coordinates [1-2 weeks] Conic sections and quadratic equations, rotations, polar coordinates, and arc length in polar coordinates. Chapter 9 - First Order Differential Equations [as time permits] (Optional) Selected topics from Sections 1 & 2: solutions, slope fields, Euler's method, first-order linear equations.

  

MATH 201. Elementary Number Theory

Instructor(s):  Section 001: Dr. A. Greicius Section 002: Dr. S. Doty

Required text(s):  Kenneth Rosen, Elementary Number Theory and its Applications, 6th Edition. ISBN-10: 0321500318; ISBN-13: 9780321500311.

Prerequisites:  Math 118

Course description:  This bridge course to higher level mathematics serves as an introduction both to number theory in particular, and to the art of mathematical argument in general. In exploring fundamental properties of integers and rational numbers, students will learn how to understand and write mathematical proofs. A central role in number theory is played by the prime numbers, whose infinitude was known already to Euclid circa 300 B.C., but whose exact distribution among integers is still so deeply mysterious now in the 21st century as to serve as the basis for secure data transmission. Topics include: representation of numbers, divisibility, prime numbers, Diophantine equations, congruence of numbers, methods of solving congruences, public-key cryptography, Fermat's Last Theorem.

  

Math 212. Linear Algebra

Instructor(s):  Section 001 - Dr A. Hupert Section 002 - Dr P. Tingley

Required text(s):  Elementary Linear Algebra by Anton (10th edition); ISBN-10: 0470458216; ISBN-13: 978-0470458211.

Prerequisites:  Math 132 or 162

Course description:  An introduction to linear algebra in abstract vector spaces with particular emphasis on Rn. Topics include: Gaussian elimination, matrix algebra, linear independence, span, basis, linear transformations, determinants, eigenvalues, eigenvectors, and diagonalization. Some of the basic theorems will be proved rigorously; other results will be demonstrated informally. Software such as Mathematica may be utilized.

  

MATH 215. [ COMP 215 ] Object-oriented programming for Math

Instructor(s):  Christine Haught

Required text(s):  Mark J. Johnson, A Concise Introduction to Programming in Python, CRC Press 2012. ISBN: 978-1-4398-9694-5.

Prerequisites:  Math 162

Course description:  Math 215 is an introductory programming course for students interested in mathematics and scientific computing. No previous programming experience is required. This course can be used to satisfy the Comp 170 requirement in the math major. Students will learn object-oriented programming using the programming language Python. Programming examples will come from mathematics, bioinformatics and other scientific computing applications. In particular we will work with examples from calculus, number theory, statistics, geometry, fractals and linear algebra. The course is programming intensive. There will be weekly programming assignments as well as frequent in-class exercises. There will be approximately 5 quizzes during the term, a final project and a final exam.

  

MATH 263. Multivariable Calculus [4 credits]

Instructor(s):  Section 001 - Dr. D. Arama Section 002 - Mr. C. Widener Section 003 - Dr. M. Bocea

Required text(s):  George Thomas, Maurice Weir, Joel Hass, Thomas’ Calculus, Multivariable (12th edition), Pearson (2009), with MyMathLab. ISBN for volume 2 + MML: 0-321-651-952

Recommended text(s):  H. M. Schey, div grad curl and all that, 4th edition, Norton & Co (2005)

Textbook notes:  Alternatively, a student may purchase MyMathLab as a separate entity and use the online version of the book. Make sure that any online purchase includes MML

Additional notes:  Required Software: Mathematica

Prerequisites:  Calculus II (Math 162) with a grade of "C-" or better

Course description:  Vectors and vector algebra, curves and surfaces in space, functions of several variables, partial derivatives, the chain rule, the gradient vector, LaGrange multipliers, multiple integrals, volume, surface area, the Change of Variables theorem, line integrals, surface integrals, Green's theorem, the Divergence Theorem, and Stokes' Theorem

  

MATH 264. Ordinary Differential Equations

Instructor(s):  Joseph Mayne

Required text(s):  Nagle, Saff, and Snider, Fundamentals of Differential Equations, 8th Edition, Pearson, 2012. ISBN-10: 0321747739.

Prerequisites:  MATH 263 with a grade of "C-" or better.

Course description:  A differential equation is often used to model a situation that involves change. Such problems as population growth, the amount of liquid flowing out of the bottom of a tank, the concentration of a drug in a patient’s bloodstream, and the position of an object dropped from above the surface of the earth can all be modeled using a differential equation. This course will concentrate on ordinary differential equations. For what equations does a solution exist and when is a solution unique? Can we solve an equation explicitly in mathematical terms? Can we find a numerical solution? What about studying equations from a qualitative viewpoint rather than a quantitative one? Topics will include first order equations, second order linear equations, Laplace Transforms, series solutions, and systems of equations. Applications to modeling will be emphasized.

  

MATH 301. History of Mathematics

Instructor(s):  Dr. Eli Maor

Required text(s):  Howard Eves, An Introduction to the History of Mathematics, 6th ed., Brooks/Cole (1990), ISBN 0030295580.

Recommended text(s):  Donald M Davis, The Nature and Power of Mathematics, 1993. Morris Kline, Mathematics - A Cultural Approach, 1962. Eli Maor, To Infinity and Beyond: A Cultural History of the Infinite, 1991.

Additional notes:  The course grade will be based on homework assignments, short presentations, a midterm exam, and a term paper on a subject of mutual consent. This class is recommended to students majoring in mathematics or science, prospective HS math teachers, and philosophy majors.

Prerequisites:  MATH 132 or 162. MATH 201 is recommended.

Course description:  This course explores selected topics in the history of mathematics from 2000 B.C.E. to the present day, including: Babylonian mathematics, Euclid's Elements, the invention of calculus, the special numbers π, e and φ, and the mathematical art of M.C. Escher.

Syllabus:  Additional or alternate topics may be included depending on the interest of students.

  

Math 304. [ Stat 304 ] Probability & Statistics I

Instructor(s):  John G. Del Greco

Required text(s):  Introduction to Mathematical Statistics and Its Applications (5th Edition) [Hardcover] Richard J. Larsen (Author), Morris L. Marx (Author)

Prerequisites:  Stat 203

Course description:  This course will be a rigorous treatment of mathematical probability with an eye toward statistics which will be the subject of the follow-up course, Stat 305. In Stat 304 we will cover axiomatic probability, combinatorial probability, conditional probability and Bayes Theorem, and independence. We will then turn to a study of random variables, both discrete and continuous, and their various distributions. Joint distributions, marginal distributions, and conditional distributions of two or more random variables will also be discussed. Advanced topics will include order statistics, moment-generating functions, and the Central Limit Theorem. Time permitting, a discussion of the Bayesian approach to probability and statistics will be included as well.

  

MATH 313. Abstract Algebra

Instructor(s):  Dr. W. Cary Huffman

Required text(s):  A First Course in Abstract Algebra, 7th Edition, John B. Fraleigh, Addison-Wesley, ISBN-10: 0201763907, ISBN-13: 9780201763904

Prerequisites:  MATH 201 or MATH 212

Course description:  Abstract algebra has its roots in the work of a brilliant group of mathematicians in the early 1800s, among them: Evariste Galois, Neils Abel, William Hamilton, and James Sylvester. Today abstract algebra plays a key role in many applications one would never have dreamed of in the nineteenth century - how do you recover errors when transmitting data in deep space communications, why do you get such clarity on your CD player, how does a bank protect its accounts from computer theft? In this course we will begin with the study of “groups”, develop many of their basic properties, and examine a large number of examples. Their study will make up the bulk of the course. We will then add a few axioms to the group axioms and obtain the structure called “rings”, which we will briefly study. Finally we will add a few more axioms to the ring axioms to obtain the “field” axioms. Groups, rings, and fields form the basic structures of abstract algebra. They also are at the heart of solutions to the problems mentioned above. The course grade tentatively will be determined from 5 quizzes, 2 exams, a final exam, and homework.

  

MATH 315. [ MATH 488 ] Advanced Topics in Linear Algebra

Instructor(s):  Dr. A. Lauve

Required text(s):  Linear Algebra Done Right, Sheldon Axler, 2nd ed., Springer (1997), ISBN: 978-0-38798-258-8

Prerequisites:  MATH 313

Course description:  An in-depth course in linear algebra with two complementary goals. (1) Abstract vector spaces and linear transformations: change of basis; similarity; duality; minimal and characteristic polynomials; eigenvectors and eigenvalues; Jordan form; bilinear forms; Cayley–Hamilton theorem; Cauchy–Binet formula; Hermitian and unitary spaces. (2) Practical matrix analysis: numerical methods; iterative techniques; location of eigenvalues; polar, singular value, QR, and LDU decompositions; Perron–Frobenius theorem; positive definite matrices; totally positive matrices; applications. Graduate students will complete more advanced exercises than the undergraduate students. In addition, they will be responsible for presenting some of the material in (2).

  

MATH 344. [ MATH 488 ] Geometry

Instructor(s):  Steven L. Jordan

Required text(s):  H. S. M. Coxeter and S.L. Greitzer, Geometry Revisited, Math Association of America, 1967, ISBN 978-0883856192; The Geometer’s Sketchpad, ver. 5, Key Curriculum Press; Student “Perpetual License” ISBN 978-1-60440-095-3.

Recommended text(s):  Euclid’s Elements, Heath tr., ISBN 978-1888009194.

Prerequisites:  Fluency in elementary Euclidean geometry.

Course description:  Geometry is indeed the pillar of mathematics: The origins of mathematics lie in the study of the heavens – i.e., in spherical trigonometry. Our knowledge and fascination with geometry has continued to this day. Perhaps the most influential textbook of all time is Euclid’s Elements. We will follow that path of study. This course is intended for prospective teachers of mathematics in high school, for math majors, and for graduate students interested in a topics course. We will make frequent use of dynamic geometry software – the most important development in the teaching of geometry in the past several decades. Topics include: points, lines, and circles associated with triangles (e.g., the 9 point circle), circle theorems, commensurability and elementary number theory, theorems of Ptolemy, Menelaus, and Bhramagupta, theorems of Pappus and Desargues, locus problems, Pascal’s Theorem, cross-ratio and inversions. We will put results from plane geometry in the larger context of perspective geometry and projective geometry, emphasizing the dualities that emerge. As time permits, we will study Poincare’s circle model of hyperbolic geometry. Graduate students in Math 488 will present such topics as combinatorial geometry, classification of polyhedra, Euclid’s development of the theory of incommensurables, Archimedes’ geometric theorems in The Sand Reckonner, Ptolemy’s model of the heavens and the Islamic geometers’ extensions, classical curves, Japanese anchor ring problems, geometric algorithms in computer graphics, spherical geometry, links, paper folding, “mechanical theorems”/centers of gravity.

  

MATH 351. Real Analysis I

Instructor(s):  Alan Saleski

Required text(s):  Arthur Mattuck, Introduction to Analysis, Prentice-Hall (1998), latest printing

Recommended text(s):  Tom Apostol, Calculus, volume I, second edition, Wiley (1967)

Prerequisites:  Math 201 and Math 212

Course description:  This course provides a rigorous development of the differential calculus. Students are expected to have had experience understanding and writing proofs. Topics covered include: numerical sequences, limit theorems for sequences, completeness property, nested intervals theorem, Bolzano-Weierstrass theorem, Cauchy sequences, infinite series, convergence tests, rearrangements, power series, functions, continuity, intermediate value theorem, compactness, uniform continuity, the derivative, mean value theorem, l'Hopital's rule, convexity, Taylor's theorem with Lagrange remainder.

  

MATH 353. Introductory Complex Analysis

Instructor(s):  Rafal Goebel

Required text(s):  Saff and Snider, Fundamentals of Complex Analysis with Applications to Engineering, Science, and Mathematics, 3rd Edition.

Prerequisites:  MATH 264 and MATH 351

Course description:  Complex analysis is essential for studying real-life problems in sciences and engineering. The course is an introduction to complex analysis, starting from basic topics like complex numbers, analytic functions, and their integration and including selected more advanced topics and applications to electrical circuits and signal processing.

  

MATH 388. [ MATH 451 ] Analysis I(MATH 451) and Measure Theory(MATH 388)

Instructor(s):  Dr. Martin Buntinas

Required text(s):  Lebesgue Measure and Integration, by Martin Buntinas. This text is available from the Department.

Prerequisites:  Real Analysis (such as MATH 351) and some Linear Algebra (such as MATH 212).

Course description:  This course will focus on measure theory, Lebesgue integration, and Fourier series. The modern theory of measure and integration was developed a little over a century ago by the French mathematician Henri Lebesgue. It completely replaced previous theories and its importance has only increased with ever widening applications. It remains today the standard form of integration used in analysis and its applications. Students should have knowledge of real analysis (equivalent to Math 351) and some acquaintance with linear algebra (equivalent to Math 212). This course is also available as MATH 388-002 for the convenience of undergraduate students. There will be two quizzes, a midterm exam, and a final exam. Homework will be assigned each class.

  

MATH 388. [ MATH 488 ] Special Topics in Math: Introduction to Partial Differential Equations

Instructor(s):  Marian Bocea

Required text(s):  Walter A. Strauss, Partial Differential Equations: An Introduction, Second Edition (2008), Wiley, ISBN-13: 978-0-470-05456-7.

Prerequisites:  MATH 263 Multivariable Calculus; MATH 264 Ordinary Differential Equations

Course description:  This is an introductory course on linear partial differential equations (PDE). A PDE is a differential equation involving derivatives of the unknown function with respect to more than one variable. Such equations model many real-world phenomena and, as such, arise in various disciplines. Typical examples are the heat equation, which governs the evolution of temperature in a conductive material, the wave equation, which governs propagation of waves, or Laplace's equation, satisfied by the stream function of an incompressible fluid. The course will serve as a conceptual introduction to the theory of PDE; although we will learn how to find explicit solutions for certain PDE (this is a problem that very often doesn't have a tractable solution, even for the simplest linear equations), the focus will be on studying qualitative properties of solutions which will help us understand phenomena encountered in applications. For example, the "maximum principle" for the heat equation explains why heat doesn't collect at "hot points". The course is primarily aimed at undergraduate Mathematics majors and MS students, but it is suitable for students majoring in Physics, Chemistry, or other disciplines, who would like to develop a more conceptual understanding of the subject. In addition to first order PDE (such as the transport equation) we will study in detail the main types of second order PDE (as illustrated by the Laplace equation, the heat equation, and the wave equation), with an emphasis on understanding the different qualitative behavior of the solutions. This will include the treatment of both homogeneous and nonhomogeneous equations and boundary conditions. We will cover selected topics from Chapters 1-7 of the textbook.

Syllabus:  A preliminary version of the syllabus is available at webpages.math.luc.edu/~mbocea/Fall2012MATH388-488.html.

  

MATH 404. [ STAT 404 ] Probability & Statistics I

Instructor(s):  Dr. Timothy E. O'Brien

Required text(s):  Mathematical Statistics with Applications, by Wackerly, Mendenhall, and Scheaffer, 7th edition (2007), Duxbury/Brooks/Cole/Thomson. ISBN-10: 0-495-11081-7.

Prerequisites:  Some background in statistics or admission into one of our Math Department's MS programs.

Course description:  This is the first semester of a two-semester sequence. The first semester is essentially an exploration of probability as a mathematical model of chance phenomena; the second semester explores the statistical analyses based on these models. In the first semester class, topics to be covered include discrete and continuous random variables, transformations, multivariate distributions, correlation, independence, variance-covariance, special distributions (binomial, Poisson, gamma, chi-square, beta, normal, multivariable normal, t and F), expectations of functions, convergence in probability, convergence in distribution, moment generating functions, and the Central Limit Theorem. Grading will be based on quizzes, exams and homework assignments; homework will be assigned on a regular basis, and collected and graded in a timely manner to provide needed feedback. This course requires a good knowledge of calculus, including sums of infinite series, differentiation, and single and double integration. Students needing a review of these concepts should co-enroll in a two-credit review class STAT 388-001.

  

MATH 451. [ MATH 388 ] Analysis I(MATH 451) and Measure Theory(MATH 388)

Instructor(s):  Dr. Martin Buntinas

Required text(s):  Lebesgue Measure and Integration, by Martin Buntinas. This text is available from the Department.

Prerequisites:  Real Analysis (such as MATH 351) and some Linear Algebra (such as MATH 212).

Course description:  This course will focus on measure theory, Lebesgue integration, and Fourier series. The modern theory of measure and integration was developed a little over a century ago by the French mathematician Henri Lebesgue. It completely replaced previous theories and its importance has only increased with ever widening applications. It remains today the standard form of integration used in analysis and its applications. Students should have knowledge of real analysis (equivalent to Math 351) and some acquaintance with linear algebra (equivalent to Math 212). This course is also available as MATH 388-002 for the convenience of undergraduate students. There will be two quizzes, a midterm exam, and a final exam. Homework will be assigned each class.

  

MATH 488. [ MATH 315 ] Advanced Topics in Linear Algebra

Instructor(s):  Dr. A. Lauve

Required text(s):  Linear Algebra Done Right, Sheldon Axler, 2nd ed., Springer (1997), ISBN: 978-0-38798-258-8

Prerequisites:  MATH 313

Course description:  An in-depth course in linear algebra with two complementary goals. (1) Abstract vector spaces and linear transformations: change of basis; similarity; duality; minimal and characteristic polynomials; eigenvectors and eigenvalues; Jordan form; bilinear forms; Cayley–Hamilton theorem; Cauchy–Binet formula; Hermitian and unitary spaces. (2) Practical matrix analysis: numerical methods; iterative techniques; location of eigenvalues; polar, singular value, QR, and LDU decompositions; Perron–Frobenius theorem; positive definite matrices; totally positive matrices; applications. Graduate students will complete more advanced exercises than the undergraduate students. In addition, they will be responsible for presenting some of the material in (2).

  

MATH 488. [ MATH 344 ] Geometry

Instructor(s):  Steven L. Jordan

Required text(s):  H. S. M. Coxeter and S.L. Greitzer, Geometry Revisited, Math Association of America, 1967, ISBN 978-0883856192; The Geometer’s Sketchpad, ver. 5, Key Curriculum Press; Student “Perpetual License” ISBN 978-1-60440-095-3.

Recommended text(s):  Euclid’s Elements, Heath tr., ISBN 978-1888009194.

Prerequisites:  Fluency in elementary Euclidean geometry.

Course description:  Geometry is indeed the pillar of mathematics: The origins of mathematics lie in the study of the heavens – i.e., in spherical trigonometry. Our knowledge and fascination with geometry has continued to this day. Perhaps the most influential textbook of all time is Euclid’s Elements. We will follow that path of study. This course is intended for prospective teachers of mathematics in high school, for math majors, and for graduate students interested in a topics course. We will make frequent use of dynamic geometry software – the most important development in the teaching of geometry in the past several decades. Topics include: points, lines, and circles associated with triangles (e.g., the 9 point circle), circle theorems, commensurability and elementary number theory, theorems of Ptolemy, Menelaus, and Bhramagupta, theorems of Pappus and Desargues, locus problems, Pascal’s Theorem, cross-ratio and inversions. We will put results from plane geometry in the larger context of perspective geometry and projective geometry, emphasizing the dualities that emerge. As time permits, we will study Poincare’s circle model of hyperbolic geometry. Graduate students in Math 488 will present such topics as combinatorial geometry, classification of polyhedra, Euclid’s development of the theory of incommensurables, Archimedes’ geometric theorems in The Sand Reckonner, Ptolemy’s model of the heavens and the Islamic geometers’ extensions, classical curves, Japanese anchor ring problems, geometric algorithms in computer graphics, spherical geometry, links, paper folding, “mechanical theorems”/centers of gravity.

  

MATH 488. [ MATH 388 ] Special Topics in Math: Introduction to Partial Differential Equations

Instructor(s):  Marian Bocea

Required text(s):  Walter A. Strauss, Partial Differential Equations: An Introduction, Second Edition (2008), Wiley, ISBN-13: 978-0-470-05456-7.

Prerequisites:  MATH 263 Multivariable Calculus; MATH 264 Ordinary Differential Equations

Course description:  This is an introductory course on linear partial differential equations (PDE). A PDE is a differential equation involving derivatives of the unknown function with respect to more than one variable. Such equations model many real-world phenomena and, as such, arise in various disciplines. Typical examples are the heat equation, which governs the evolution of temperature in a conductive material, the wave equation, which governs propagation of waves, or Laplace's equation, satisfied by the stream function of an incompressible fluid. The course will serve as a conceptual introduction to the theory of PDE; although we will learn how to find explicit solutions for certain PDE (this is a problem that very often doesn't have a tractable solution, even for the simplest linear equations), the focus will be on studying qualitative properties of solutions which will help us understand phenomena encountered in applications. For example, the "maximum principle" for the heat equation explains why heat doesn't collect at "hot points". The course is primarily aimed at undergraduate Mathematics majors and MS students, but it is suitable for students majoring in Physics, Chemistry, or other disciplines, who would like to develop a more conceptual understanding of the subject. In addition to first order PDE (such as the transport equation) we will study in detail the main types of second order PDE (as illustrated by the Laplace equation, the heat equation, and the wave equation), with an emphasis on understanding the different qualitative behavior of the solutions. This will include the treatment of both homogeneous and nonhomogeneous equations and boundary conditions. We will cover selected topics from Chapters 1-7 of the textbook.

Syllabus:  A preliminary version of the syllabus is available at webpages.math.luc.edu/~mbocea/Fall2012MATH388-488.html.

  

STAT 103. Fundamentals of Statistics

Required text(s):  Freedman, Pisani, Purves, Statistics, 4th edition. ISBN-13 978-0-393-92972-0

Prerequisites:  None

Course description:  An introduction to statistical reasoning. Students learn how statistics has helped to solve major problems in economics, education, genetics, medicine, physics, political science, and psychology. Topics include: design of experiments, descriptive statistics, mean and standard deviation, the normal distribution, the binomial distribution, correlation and regression, sampling, estimation, and testing of hypothesis. A TI-83 (or equivalent) calculator is required for this course

Syllabus:  1. Introduction (Chapters 1 and 2) a) Controlled Experiments b) Observational Studies 2. Descriptive Statistics (Chapters 3-6) a) Histograms b) Mean and Standard Deviation c) Normal Approximation for Data d) Measurement Error 3. Chance Variability (Chapters 16-18) a) Law of Averages b) Expected Value and Standard Error c) Normal Approximation for Probability Histograms 4. Sampling (Chapters 19-21, 23) a) Sample Surveys b) Chance Errors in Sampling c) Accuracy of Percentages d) Accuracy of Averages 5. Tests of Significance (Chapters 26-27) a) Hypothesis Tests b) More Tests for Averages 6. Correlation and Regression (Chapters 8-12) a) Correlation b) More Correlation c) Regression d) R.M.S. Error for Regression e) Regression Line Supplemental topics chosen from the following, if time allows: 7. Probability (Chapters 13-14) 8. More Hypothesis Tests (Chapters 28-29)

  

STAT 203. Statistics

Instructor(s):  Dr. M. Walsh

Required text(s):  Buntinas and Funk, Statistics for the Sciences, Thomson/Brooks/Cole, 2005, ISBN: 0-534-38774-8

Prerequisites:  MATH 132 or 162

Course description:  Our society is increasingly dependent upon statistics. For example, decisions about the safety and effectiveness of drugs, changes in tax laws that affect the economy, and environmental regulations that strive to improve our lives all involve the use of statistics. In spite of this importance, there is widespread ignorance about the proper application of statistics. In this course we will look at examples of the use and misuse of statistics using methods of differential and integral calculus to justify results. We will study some standard statistical methods and learn how to determine when they should be used and how they should be applied. The goal is to understand how these methods work and how they can be applied correctly

  

STAT 303. SAS Programming and Applied Statistics

Instructor(s):  Dr. Michael Perry

Required text(s):  R. Cody & Smith, Applied Statistics and the SAS Programming Language, 5th ed., Prentice-Hall.

Prerequisites:  Stat 103 or 203 or 335

Course description:  This course is an introduction to writing and executing SAS programs under the Windows environment in the context of applied statistics problems. SAS procedures are used to read and analyze various types of data sets as they apply to t-tests, simple and multiple regressions, ANOVA, categorical analysis, and repeated measures.

  

Stat 304. [ Math 304 ] Probability & Statistics I

Instructor(s):  John G. Del Greco

Required text(s):  Introduction to Mathematical Statistics and Its Applications (5th Edition) [Hardcover] Richard J. Larsen (Author), Morris L. Marx (Author)

Prerequisites:  Stat 203

Course description:  This course will be a rigorous treatment of mathematical probability with an eye toward statistics which will be the subject of the follow-up course, Stat 305. In Stat 304 we will cover axiomatic probability, combinatorial probability, conditional probability and Bayes Theorem, and independence. We will then turn to a study of random variables, both discrete and continuous, and their various distributions. Joint distributions, marginal distributions, and conditional distributions of two or more random variables will also be discussed. Advanced topics will include order statistics, moment-generating functions, and the Central Limit Theorem. Time permitting, a discussion of the Bayesian approach to probability and statistics will be included as well.

  

STAT 307. Statistical Design and Analysis of Experiments

Required text(s):  Statistical Analysis of Designed Experiments: Theory and Applications by Ajit C. Tamhane, John Wiley & Sons, Inc (2009) ISBN 978-0-471-75043-7

Recommended text(s):  Optimal Design of Experiments A Case Study Approach, by Peter Goos and Bradley Jones, John Wiley & Sons, Ltd

Prerequisites:  STAT 203 or 335

Course description:  Why study the theory of experiment design? A specific design can seldom be used without adapting it to the specific the circumstances of the experiment. Successful designs adapt general theoretical principles to the specific circumstances of each individual application. This course focuses on the underlying concepts of experimental design and the statistical structure developed from these concepts. These ideas are illustrated with applications from many areas: biometric applications, clinical trials, environmental research, marketing, engineering, education, etc. Topics include comparative experiments, analysis of variance, fixed, random and mixed effects models, randomized block designs, Latin square designs, incomplete block designs, and fractional factorial designs. Use of packaged computer programs such as MINITAB, R or SAS.

  

STAT 308. Applied Regression Analysis

Instructor(s):  Dr. Changwon Lim

Required text(s):  Introduction to Regression Modeling (with CD-ROM), by Bovas Abraham & Johannes Ledolter, Thomson Brooks/Cole (2006); ISBN 978-0-534-42075-8.

Prerequisites:  STAT 203 or 335.

Course description:  Simple and multiple linear regression methods including weighted least squares and polynomial regression. Multiple comparison estimation procedures, residual analysis, and other methods for studying the aptness of a proposed regression model. Use of packaged computer programs such as Minitab, SPSS and SAS.

  

STAT 310. Categorical Data Analysis

Instructor(s):  Dr. Molly Walsh

Required text(s):  An Introduction to Categorical Data Analysis, 2nd Ed, by Alan Agresti (2007), John Wiley & Sons, ISBN: 978-0-471-22618-5.

Prerequisites:  STAT203 or STAT335 or equivalent, or permission of instructor.

Course description:  Normally distributed response variables lead statistical practitioners to use simple linear models procedures such as simple and multiple regression or one- or two-way ANOVA, but other types of data cannot be analyzed in the same ways. Thus, these simple (regression) techniques have been generalized to handle nominal, ordinal, count and binary data under the general heading of categorical data analysis. Contingency table analyses, generalized linear models, logistic regression and log-linear modeling are the focus of this course. This course also addresses the fundamental questions encountered with regression and ANOVA for count data. Specialized methods for ordinal data, small samples, multi-category data, matched pairs, marginal models and random effects models will also be discussed. The focus throughout this course will be on applications and real-life data sets; as such, theorems and proofs will not be emphasized.

  

STAT 335. [ BIOL 335 ] Introduction to Biostatistics [4 credit hours]

Instructor(s):  Section 001: Mr. B. Longman Section 002: Mr. B. Longman Section 003: Dr. M. Walsh Section 005: Dr. M. Walsh

Required text(s):  Myra L. Samuels and Jeffrey A. Witmer, Statistics for the Life Sciences, Prentice Hall, 4th edition Prentice Hall (2012), ISBN: 10-0-321-65280-0; 13: 978-0-32165280-5

Additional notes:  Students may not receive credit for both STAT 203 & 335

Prerequisites:  Calculus II (Math 162 or 132); Introduction to Biology II (Biol 102)

Course description:  An introduction to statistical methods used in designing biological experiments and in data analysis. Topics include frequency distributions, probability and sampling distribution, design of biological experiments, interval estimation, tests of hypotheses, analysis of variance, correlation and regression. This course will have two quizzes, two exams, regularly assigned homework and computer laboratory assignments in MINITAB with biological data.

  

STAT 335. Intro to Biostatistics

Instructor(s):  Bret A. Longman

Required text(s):  Samuels, Witmer, Schaffner. Statistics for the Life Sciences. 4th edition, Prentice Hall, 2012. Print

Prerequisites:  MATH 162 or 132; BIOL 102

Course description:  An introduction to statistical methods used in designing biological experiments and in data analysis. Topics include probability and sampling distribution, design of biological experiments and analysis of variance, regression and correlation, stochastic processes, and frequency distributions. Computer laboratory assignments with biological data.

  

STAT 388. Calculus for Graduate Students

Instructor(s):  Dr. Martin Buntinas

Required text(s):  None

Prerequisites:  None

Course description:  This is a two-credit supplemental course that will meet during the fall semester. a. If you have never taken a course in multivariable calculus, then this supplemental course is REQUIRED. b. If you have forgotten a lot of multivariable differentiation and integration, then the supplemental course is HIGHLY recommended. Here are some topics that will be covered in STAT 388-001: A review of calculus, convergence, sequences and series, Taylor series, differentiation and integration of functions of several variables, linear algebra, shortcuts and tricks of the trade. There is no textbook required for STAT 388-001. However, your old calculus textbooks could be handy references. Mostly, we will work problems that are typical in theoretical probability and statistics. This course is graded based on participation in the class.

  

STAT 388. [ STAT 488 ] Topic: Intro Nonparametric Statistics

Instructor(s):  (Section 002) Dr. Changwon Lim

Required text(s):  Applied Nonparametric Statistical Methods, by Sprent and Smeeton, 4th edition (2007), Chapman and Hall/CRC; ISBN-10: 1-58488-701-X

Prerequisites:  STAT203 or STAT335 or equivalent, or permission of instructor.

Course description:  This course covers basic standard nonparametric statistical methods – that is, techniques designed when normal-based methods are questionable or not valid. From this distribution-free perspective, the course covers one-, two- and several sample methods, correlation and regression, and simulation techniques. The emphasis of the course is on applications although some theoretical results are developed. Students are required to analyze real-life datasets using the Minitab, SAS and R statistical packages (although no previous programming experience is assumed). Grading will be based on homework assignments, quizzes, exams, and a course project.

  

Stat 403. SAS Program & Appl Stat

Instructor(s):  Liping Tong

Required text(s):  R. Cody & Smith, Applied Statistics and the SAS Programming Language, 5th ed., Prentice-Hall.

Recommended text(s):  Geoff Der and Brian S. Everitt, Statistical Analysis of Medical Data Using SAS, Chapman and Hall / CRC (2006).

Textbook notes:  Programs (and handouts) in Cody and Smith's book as well as solutions to odd numbered problems are available at www.prenhall.com/cody. Examples and data sets for Geoff and Everitt's book are available at support.sas.com/documentation/onlinedoc/code.samples.html.

Prerequisites:  The prerequisites are courses covering sampling distributions, confidence intervals, hypothesis tests such as T-tests, chi-square tests, etc., linear regressions and ANOVA.

Course description:  This course is an introduction to the use of statistical software SAS, one of many different statistical packages on the market. What SAS offers over many other packages is its outstanding database management capabilities. In part for this reason SAS is one of the most popular statistical packages in government and industry. SAS runs on a variety of platforms, we will use the Windows environment. In addition to data management, we will also focus on applications and explanations of SAS output. For more information on SAS you can visit sas.com.

  

STAT 404. [ MATH 404 ] Probability & Statistics I

Instructor(s):  Dr. Timothy E. O'Brien

Required text(s):  Mathematical Statistics with Applications, by Wackerly, Mendenhall, and Scheaffer, 7th edition (2007), Duxbury/Brooks/Cole/Thomson. ISBN-10: 0-495-11081-7.

Prerequisites:  Some background in statistics or admission into one of our Math Department's MS programs.

Course description:  This is the first semester of a two-semester sequence. The first semester is essentially an exploration of probability as a mathematical model of chance phenomena; the second semester explores the statistical analyses based on these models. In the first semester class, topics to be covered include discrete and continuous random variables, transformations, multivariate distributions, correlation, independence, variance-covariance, special distributions (binomial, Poisson, gamma, chi-square, beta, normal, multivariable normal, t and F), expectations of functions, convergence in probability, convergence in distribution, moment generating functions, and the Central Limit Theorem. Grading will be based on quizzes, exams and homework assignments; homework will be assigned on a regular basis, and collected and graded in a timely manner to provide needed feedback. This course requires a good knowledge of calculus, including sums of infinite series, differentiation, and single and double integration. Students needing a review of these concepts should co-enroll in a two-credit review class STAT 388-001.

  

STAT 407. Statistical Design and Analysis of Experiments

Instructor(s):  Gerald M. Funk

Required text(s):  Statistical Analysis of Designed Experiments Theory and Applications, by Ajit C. Tamhane, John Wiley & Sons, Inc (2009) ISBN 978-0-471-75043-7; Optimal Design of Experiments A Case Study Approach, by Peter Goos and Bradley Jones, John Wiley & Sons, Ltd © 2011 ISBN: 978-0-470-74461-1, or as e-book ISBN: 978-1-1199-7616-5.

Prerequisites:  Some background in basic statistical methods or biostatistics, or permission of instructor.

Course description:  Why study the theory of experiment design? A specific design can seldom be used without adapting it to the specific the circumstances of the experiment. Successful designs adapt general theoretical principles to the specific circumstances of each individual application. This course focuses on the underlying concepts of experimental design and the statistical structure developed from these concepts. These ideas are illustrated with applications from many areas: biometric applications, clinical trials, environmental research, marketing, engineering, education, etc. Topics include comparative experiments, analysis of variance, fixed, random and mixed effects models, randomized block designs, Latin square designs, incomplete block designs, and fractional factorial designs. Use of packaged computer programs such as MINITAB, R or SAS.

  

STAT 408. Applied Regression Analysis

Instructor(s):  Dr. Changwon Lim

Required text(s):  Introduction to Regression Modeling (with CD-ROM) by Bovas Abraham & Johannes Ledolter, Thomson Brooks/Cole (2006). ISBN 978-0-534-42075-8.

Prerequisites:  Some background in basic statistical methods or biostatistics, or permission of instructor.

Course description:  This course provides students with a thorough introduction to applied regression methodology. The concept of simple linear regression will be reviewed and discussed using matrices, and multiple linear regression, transformations, diagnostics, polynomial regression, indicator variables, model building and multicollinearity will be discussed, as will be nonlinear and generalized linear regression. The course will focus on applications such as those from biometry and biostatistics (clinical trials, HIV studies, etc.), sports, engineering, agriculture and environmental science.

  

STAT 488. [ STAT 388 ] Topic: Intro Nonparametric Statistics

Instructor(s):  (Section 002) Dr. Changwon Lim

Required text(s):  Applied Nonparametric Statistical Methods, by Sprent and Smeeton, 4th edition (2007), Chapman and Hall/CRC; ISBN-10: 1-58488-701-X

Prerequisites:  STAT203 or STAT335 or equivalent, or permission of instructor.

Course description:  This course covers basic standard nonparametric statistical methods – that is, techniques designed when normal-based methods are questionable or not valid. From this distribution-free perspective, the course covers one-, two- and several sample methods, correlation and regression, and simulation techniques. The emphasis of the course is on applications although some theoretical results are developed. Students are required to analyze real-life datasets using the Minitab, SAS and R statistical packages (although no previous programming experience is assumed). Grading will be based on homework assignments, quizzes, exams, and a course project.

  

STAT 488. Statistical Consulting

Instructor(s):  Dr. Timothy O'Brien

Required text(s):  Javier Cabrera and Andrew McDougall, Statistical Consulting, Springer-Verlag, 2002; ISBN: 0-387-98863-7).

Prerequisites:  One year of MS full-time study in the Applied Statistics program (prerequisites or co-requisites including regression and methods such as those covered in SAS and design classes – categorical data analysis and/or survival analysis also recommended), or obtain the permission of the instructor.

Course description:  This course serves as a program capstone course in the sense of synthesizing the material in first-year courses in the context of actual statistical consulting sessions. Students are required to assist in analyzing real-life data sets using the Minitab, SAS and R statistical packages. Students also learn to sharpen their verbal, written and non-verbal communication skills. Grading is based on homework assignments, in-class presentations and consulting sessions/practicum, and a course project.