The Department of Computer Science, Mathematics, and Engineering

MATH - Mathematics

A systematic approach to organized reasoning by study of the rudiments of logic. Study of the structure of various mathematical systems and operations defined on these systems. An analysis and discussion of the uses of such systems. The counting techniques of permutations and combinations may be considered.**Prerequisites:** ACFN 070 and ACFN 080, or ACFN 090 or satisfactory placement score

Topics in University algebra include properties of the real numbers; radicals and rational exponents; operations on polynomials and rational expressions; solution of linear and quadratic equations and inequalities; functions, including graphs and composite functions; properties of linear functions; and systems of two linear equations and inequalities. This course does not fulfill the general studies requirement in mathematics. **Prerequisites:** ACFN 070 and 080, or ACFN 090 or satisfactory placement score

A study of the trigonometric functions and identities, multiple angle formulas, inverse trigonometric functions, deMoivre's theorem and complex numbers, applications. **Prerequisite:** MATH 105 or satisfactory placement score

Topics in algebra which will prepare students for the study of calculus, including complex numbers, graphs of nonlinear functions and relations, conic sections, graphical and algebraic solutions of nonlinear equations, solutions of exponential and logarithmic equations, introduction to analytic geometry, sequences, series, summations, and mathematical induction. **Prerequisite:** MATH 105 or satisfactory placement score

This course examines principles of interest and discount, annuities and insurance, amortization, bonds and similar topics. This course does not fulfill the general studies requirement in mathematics. **Prerequisite:** Satisfactory placement score

Mathematical models for the analysis of decision-making problems are examined. Topics include the echelon method for solving linear equations, matrix manipulations, optimization by linear programming including the simplex method, risk decisions using probability, expected value, and statistics. Additional topics may be chosen from network models or game theory. **Prerequisites:** ACFN 070 and ACFN 080, or ACFN 090 or MATH 105 or satisfactory placement score

Topics in this course include solutions for a system of linear equations, matrix algebra, optimization problems and duality, counting arguments, combinations and permutations, elementary probability theory, Markov chains, elementary graph theory, and other applications arising out of finite mathematics.**Prerequisites:** MATH 105 or satisfactory math placement. Students in the Department of Computer Science, Mathematics, and Engineering must use this course instead of MATH 154 as the general studies requirement.

This course explores the fundamental ideas of planar and spatial geometry. Content includes the analysis and classification of geometric figures; the study of geometry transformations; the concepts of tessellation, symmetry, congruence, and similarity; connection of geometry to other mathematical topics and to nature and art; and an overview of measurement. The course also includes an introduction to the use of computers in the teaching and learning of informal geometry. **Prerequisites:** MATH 102 or permission of instructor.

Topics in differential and integral calculus, with stress on their applications in business, biology, social, and behavioral sciences. **Prerequisite:** MATH 108 or satisfactory math placement test score.

Fundamental concepts of calculus, using analytic geometry. After preliminaries about the real number system, intervals, and functions, properties of limits are carefully stated. These are used to develop standard differentiation formulas. Applications of the derivative [as a rate of change] are stressed in a wide variety of problems. Introduction to integration via anti-differentiation and area and the fundamental theorem. Applications of the integral [volumes, arc length, surface area, etc.] **Prerequisite:** MATH 106 and MATH 108 or satisfactory math placement score.

Continuation of MATH 207. Calculus of exponential, logarithmic, and trigonometric functions; techniques of integration. Review of conic sections in standard form and in rotation. Polar coordinates, l'HĂ´pital's rule, improper integrals, infinite series, and Taylor series. **Prerequisite:** MATH 207

A study of numerical methods for interpolation, approximation, root finding, differentiation, integration, and linear and nonlinear systems. Computer algorithm development and error analysis will be emphasized. **Prerequisite/corequisite:** MATH 208

Topics from modern mathematics with particular emphasis on those with applications to computer science. Logic, sets, number systems and number theory, enumeration, graphs and trees, matrices, finite algebraic systems, and analysis of algorithms are examined. **Prerequisite:** MATH 154 or MATH 155 or MATH 205 or MATH 207

Classical introduction to Aristotelian logic using truth tables or Venn diagrams. Application to Boolean arithmetic and algebra. Positive and negative logic as in gate structures for digital circuits. **Prerequisite:** MATH 105, MATH 154, or MATH 101

Practical experience in teaching mathematics will be provided in a tutorial setting, under the guidance and supervision of a faculty member. Two or three hours of student-tutor interaction will be arranged each week. **Prerequisite:** MATH 207

An in-depth study of the elementary curriculum content examining methods, problems, and techniques involved in mathematics instruction. **Prerequisite:** MATH 102 and MATH 200.

The course begins with a study of linear systems, using matrices and determinants to solve them. Vector spaces are treated axiomatically and discussed geometrically. Linear transformation of vector spaces and their matrix representations are considered. Finally eigenvectors and eigenvalues are considered with applications. **Prerequisites:** MATH 154 or MATH 254, and MATH 207 or MATH 205

Continuation of MATH 208. Vectors in the plane and in space, parametric equations, solid analytic geometry. Calculus of functions of several variables including partial derivatives, multiple integrals, and their applications. **Prerequisite:** MATH 208

Examines first order ordinary differential equations [e.g. exact, separable, Bernoulli, homogeneous], direction field, numerical solution; higher order equations including the methods of Lagrange and undetermined coefficients; Laplace transforms; systems of first order equations; introduction to Fourier series; and applications in the physical and biological sciences. **Prerequisite:** MATH 208 and MATH 307

Introduction to algebraic structures such as groups, rings, and fields. Formal development of their properties, complemented by examples and applications. **Prerequisites:** MATH 208, MATH 307, and MATH 254.

This is a first course in statistics, primarily for those needing knowledge of statistical methods and the interpretation of statistical data. It discusses basic probability ideas, then deals with frequency distributions, measures of central tendency and dispersion; hypothesis testing using z, t, and chi-square tests; correlation, linear regression, and one-way ANOVA. For reinforcement, students must complete several laboratory assignments using statistical software. Students may not receive credit for both this course and BADM 224. **Prerequisite:** MATH 105 or permission of chair.

A laboratory-based course treating topics in mathematics using a "computer algebra" system. A study of the fundamentals of a symbolic manipulator system, such as Mathematica and Maple, which can display factoring as well as derivative and integral formulas. Applications include solution of problems arising in calculus, graph theory, number theory, statistics, and sciences. **Prerequisite:** MATH 207 or 205

A study of numerical methods applied to such problems as the solutions of equations, interpolation, differentiation, integration, and solution of differential equations. Emphasis on obtaining solutions with computer programs.**Prerequisite:** MATH 218, MATH 307, and MATH 310.

Topics include axioms for probability; random variables, discrete and continuous probability distributions; expected value; functions of random variables; covariance; conditional probability; independence; confidence intervals; tests of hypotheses: normal, t, signed-rank, chi-square tests; linear regression and correlation. **Prerequisite:** MATH 309

Aimed at applications, primarily from the environmental sciences, this course is designed to explicitly demonstrate the ways mathematics is used to solve problems arising in the natural sciences and in other walks of life as well. A wide variety of phenomena in nature can be described by what one calls a mathematical model. This may involve statistics, differential equations, computer simulation, algebraic and combinatorial structures. River and lake pollution, spread of an epidemic, population growth, solar energy, and vibration, as well as several economics, chemistry, and political science models will be studied. **Prerequisites:** MATH 318, MATH 321, and MATH 310.

An introduction to main topics of operations research: linear programming, network optimization, dynamic programming, and queueing theory. The simplex algorithm will be studied in details, including duality theory and sensitivity analysis. In network optimization the OSPF algorithm, PERT, and CPM will be considered. Examples of applications from industry, notably some queueing algorithms. Additional topics may be chosen from Markov chains, integer programming, nonlinear programming, game theory and decision analysis, and simulation. **Prerequisite:** MATH 154 and MATH 207 or MATH 254

Cooperative Education is a form of education which integrates classroom study with paid, planned, and supervised work experiences in the public and private sectors. Cooperative education allows students to acquire essential, practical skills by being exposed to the reality of the work world beyond the boundaries of campus, enhancing their self-confidence and career direction. Co-ops may extend beyond the semester and may be paid positions. A co-op must have an academic component. A cooperative education agreement is signed by the employer supervisor, the faculty supervisor, and the student. The co-op may be repeated for credit, but not in the same term; the topic must be different. **Prerequisites:** Sophomore standing; minimum 2.5 overall GPA; approval of Mathematics and Engineering Department; placement by Career Center

An introductory course in number theory with emphasis on the classical theorems and problems. **Prerequisite:** MATH 307 or MATH 312

A course designed to acquaint the advanced student with certain topics outside the traditional course in mathematics. **Prerequisite:** Consent of instructor

The course begins with the arithmetic of complex numbers, including powers, roots, and polar representation, with special emphasis on the geometric view. Several function classes are studied in the setting of the complex plane, especially linear, linear fractional, exponential, logarithmic, and trigonometric. Includes basic notions from calculus, particularly limits, continuity, and the derivative, are reexamined in the complex setting. Special attention is given to the properties of analytic functions, harmonic functions, and the Cauchy-Riemann equations. Applications are considered in areas such as steady state temperature patterns and electrostatic potentials. The latter part of the course deals with contour integration techniques, power series representation, and the classic theorems on analytic functions of a complex variable. **Prerequisite:** MATH 309 or permission of instructor

A thorough examination of the fundamentals of elementary calculus and its extensions, with emphasis on interrelation with other areas of mathematics, and upon various applications. **Prerequisites:** MATH 309; MATH 307 or MATH 312

See BADM 413 in Business Administration course listings.

A capstone course requiring mathematical maturity. A survey of mathematical topics dating from ancient times, with emphasis on the development of numbers, algebra, theory of planetary motion, and non-Euclidean geometry. In preparation for a comprehensive test, a structured review of core mathematical ideas and techniques will be included. **Prerequisites:** MATH 208 and MATH 312, or permission of instructor.

Study of the properties of regions unaffected by continuous mappings. Includes consideration of open and closed sets, interior and boundary of a set, and neighborhood systems; motivation for concrete applications of the idea of a topological space and its separation properties. Other topics may include various applications of the notions of convergence and compactness. **Prerequisites:** MATH 207; MATH 307 or MATH 312

This course is a brief introduction to methods of solving partial differential equations [PDE] using Green's Function, Fourier Series, etc. In particular, heat and wave equations will be studied in more details. Some nonlinear PDE may be considered as well. **Prerequisites:** MATH 309 and MATH 310. Corequisite: MATH 409.

A careful axiomatic development of certain parts of elementary Euclidean and non-Euclidean geometry. The examination of the axiomatic method as an important pattern of thought. **Prerequisite:** MATH 307, MATH 254, and MATH 309.

This course will focus on various theoretical concepts in number theory and combinatorics, with a view in mind to applications such as elliptic curve cryptography, Reed-Solomon codes, credit card validation, and statistical applications of balanced incomplete block designs.

Students learn methods and skills for the engineering design process, demonstrate the ability to explore principles of engineering experimentation and design, identify real world projects in multidisciplinary engineering areas, and develop a practical plan to complete the projects [individual and/or group]. Approved written project proposals and oral presentations are required at the end of the semester. The written proposal should include problem descriptions, objectives, selected approach, design alternatives, equipment requirements, and timeline, as well as ethical, legal, and environmental issues. Pass/fail grade. **Prerequisites:** Junior or Senior standing and permission of the instructor.

Students develop and complete the proposed projects by utilizing the knowledge and experience gained from previous courses and by demonstrating the analyses and experiments. Students are required to present work in a professional manner which consists of three parts: comprehensive written reports including research and analysis, oral presentations, and operating working models. **Prerequisites:** MATH 489

Course Number | 2017-18 |
2018-19 |
2019-20 |
2020-21 |
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FA | SP | FA | SP | FA | SP | FA | SP | |

MATH 100 | X | X | X | X | ||||

MATH 300 | X | X | X | X | X | X | X | |

MATH 307 | X | X | X | X | ||||

MATH 309 | X | X | X | |||||

MATH 310 | X | X | X | |||||

MATH 312 | X | X | X | X | ||||

MATH 314 | X | X | X | X | X | X | X | |

MATH 318 | X | X | X | |||||

MATH 321 | X | X | X | |||||

MATH 329 | X | X | X | X | ||||

MATH 354 | X | X | X | |||||

MATH 409 | X | X | ||||||

MATH 410 | X | X | X | |||||

MATH 414 | X | X | X | X | ||||

MATH 424 | X | X | X | X | ||||

EDUC 489 | X | X | X | X | ||||

MATH 490 | X | X | X | |||||

EDUC 420 | See Advisor or Dept Chair |
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DATA 118 | X | X | X | X | ||||

DATA 418 | X | X | X |