Exploring Discrete Mathematics Courses at Queens College
Queens College offers a diverse range of discrete mathematics courses designed to equip students with the fundamental mathematical concepts and skills essential for success in various fields, including computer science, mathematics, education, and more. These courses cater to different levels of mathematical maturity and career aspirations, providing a pathway for students to delve deeper into the world of discrete mathematics.
Foundational Courses
MATH 110: Mathematical Literacy
MATH 110, also known as Mathematical Literacy, emphasizes the importance of mathematical literacy in today’s highly technological society. Students will gain hands-on experience in solving real world problems in such diverse areas as law, medicine, and politics. Applications include analysis of election results and voting schemes, interpretation of medical data, and study of the nature of fair political representation. Mathematical topics covered will include an introduction to probability and statistics through normal curves and confidence intervals; exponential and logistic growth models; and the algebraic skills necessary for all the applications covered. Extensive use will also be made of today’s sophisticated graphing calculators. Successful completion of the course satisfies the Basic Skills Requirement in Mathematics and prepares students for MATH 113, 114, 116, and 119.
MATH 113: Explorations in Mathematics
MATH 113 explores several areas of mathematics to give the student an appreciation of the significance of mathematics, both in terms of its applications and of its place in the history of civilization.
MATH 114/114W: Introduction to Probability and Statistics
MATH 114 serves as an introduction to mathematical probability and statistics for the general student. Note that it is not open to mathematics, physics, or chemistry majors, or to students who are taking or have passed MATH 114W, 241, 611, 621, 633, BIOL 230, ECON 249, PSYCH 107, SOC 205, 206, 207.
MATH 114W is a 4-credit, writing-intensive version of MATH 114. It includes the material in MATH 114, as well as additional topics such as sampling methods, research design, and composing and conducting surveys, explored through student research and writing assignments. Similar to MATH 114, it is not open to mathematics, physics, or chemistry majors, or to students who are taking or have passed MATH 114, 241, 611, 621, 633, BIOL 230, ECON 249, PSYCH 107, SOC 205, 206, 207.
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MATH 115: Algebra and Mathematical Models
MATH 115 covers topics including linear, polynomial, rational, and radical expressions as mathematical models; solving equations and systems of equations that arise through the application of these models. It is not open to students who are taking or have received credit, including transfer credit or advanced placement credit, for any precalculus or calculus course.
MATH 116
MATH 116 has 3 hr.; 3 cr.
MATH 119: Mathematics for Elementary School Teachers
MATH 119 is designed to make prospective elementary school teachers aware of the beauty, meaning, and relevance of mathematics.
MATH 120: Discrete Structures for Computer Science
MATH 120 provides fluency in foundational mathematical concepts that appear in future courses in computer science. This course is intended for computer science majors; it does not count toward a major or minor in mathematics. Topics include sets, basic combinatorics, functions, sequences, series, products, logarithms, divisibility, and modular arithmetic.
MATH 122: Precalculus and Introduction to Calculus Topics
MATH 122 offers a thorough introduction to the topics required for calculus. Topics include real and complex numbers, algebra of functions, the fundamental theorem of algebra, trigonometry, logarithms, and exponential functions, conic sections, and the use of graphing calculators. Students unsure of their preparation for calculus are advised to take the Queens College mathematics placement test. Not open to students who have received credit, including transfer credit or advanced placement credit, for any calculus course.
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MATH 128: Mathematics and Digital Art
MATH 128 focuses on programming computers to create digital art based on mathematical exploration of two dimensional geometry. Topics include transformations of the plane, trigonometric functions, polar coordinates, parametric functions, and Mobius transformations.
MATH 131: Calculus I for Non-Science Students
MATH 131 introduces the fundamental ideas and techniques of calculus to nonscience students. Special emphasis is given to applications. Topics include functions and graphs; derivatives and differentiation techniques; the marginal concept in economics; optimization methods; compound interest; exponential and logarithmic functions. Not open to students who are taking any other calculus course or have received credit, including transfer credit or advanced placement credit, for any calculus course.
MATH 132: Calculus II for Non-Science Students
MATH 132 is a continuation of MATH 131. Topics include limits and continuity; mean value theorem; antiderivatives; integrals and integration techniques; applications of the definite integral; the calculus of logarithmic, exponential, and trigonometric functions. This course prepares students who have taken MATH 131 to continue into MATH 143.
MATH 141: Calculus I (Part 1)
MATH 141 is the first part of a three-semester sequence (MATH 141, 142, 143) covering the same material as MATH 151 and 152. Credit is given for each course satisfactorily completed; a student need not take the entire sequence. Not open to students who are taking any other calculus course or have received credit, including transfer credit or advanced placement credit, for any calculus course. It requires MATH 122, or permission of the department.
MATH 142: Calculus I (Part 2)
MATH 142 is a continuation of MATH 141. Not open to students who are taking any other calculus course or have received credit, including transfer credit or advanced placement credit, for any calculus course other than MATH 141 or MATH 151.
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MATH 143: Calculus II (Part 3)
MATH 143 requires MATH 142 or MATH 132, min grade C-, or permission of the department. A continuation of MATH 142. Not open to students who are taking any other calculus course or have received credit, including transfer credit or advanced placement credit, for any calculus course other than MATH 131, MATH 132, MATH 141, MATH 142 or MATH 151.
MATH 151: Calculus I
MATH 151 is the first part of a two-semester sequence (MATH 151 and 152) intended for students who want to study mathematics, physics, chemistry, or engineering. Credit is given for each course satisfactorily completed; a student need not take the entire sequence. Students who want a less rapid introduction to calculus should take MATH 141. Topics include sets, inequalities, straight lines, circles, functions, limits, continuity, the derivative, formulas of differentiation, implicit differentiation, velocity, acceleration, maxima and minima, Rolle’s theorem, the mean value theorem, points of inflection, curve sketching, and antiderivatives. Not open to students who are taking any other calculus course or have received credit, including transfer credit or advanced placement credit, for any calculus course. Not open to students who have received either a D or F in MATH 141.
MATH 152: Calculus II
MATH 152 deals with several aspects of differential and integral calculus. Among the topics studied are the definite integral, applications of the definite integral, the differentiation of logarithmic, exponential, and inverse trigonometric functions, integration, indeterminate forms, improper integrals, infinite series, and expansions of functions. Applications to problems of geometry and physics. Not open to students who are taking any other calculus course or have received credit, including transfer credit or advanced placement credit, for any calculus course other than MATH 151.
MATH 172: Introduction to SQL and Data Visualization
MATH 172 introduces the fundamentals of Structured Query Language (SQL), relational database management systems, and data visualization.
MATH 190: Special Topics
MATH 190's topic is announced in advance. May be repeated for credit if topic is different.
Advanced Courses
MATH 201: Calculus III
MATH 201 requires MATH 143 OR 152, MIN GRADE C-. A continuation of the work of MATH 143 or 152. The topics include polar coordinates, vectors, solid analytic geometry, vector valued functions, double and triple integrals, functions of several variables, partial derivatives. Wherever possible, applications are made to problems of geometry and physics.
MATH 202
MATH 202 has 4 hr.; 4 cr.
MATH 205: Mathematical Problem Solving
MATH 205 presents techniques and develops skills for analyzing and solving problems mathematically and for proving mathematical theorems. Students will learn to organize, extend, and apply the mathematics they know and, as necessary, will be exposed to new ideas in areas such as geometry, number theory, algebra, combinatorics, and graph theory. Prereq.
MATH 209: Set Theory
MATH 209 covers basic axioms of set theory, algebra of sets, relations and functions, orders, countable and uncountable sets, and additional topics at the discretion of the instructor. The course will introduce some basic proof techniques, with no background in proof-writing assumed.
MATH 218: Advanced Euclidean Geometry
MATH 218 is a course in advanced Euclidean geometry for current and prospective mathematics teachers that will provide mathematical background for teaching geometry in secondary schools. The course will focus on definitions, theorems, existence proofs, and constructions.
MATH 220: Discrete Mathematics
MATH 220 delves into discrete structures including sets, relations, and functions. Enumeration. Propositional and predicate logic. Proof techniques. Graphs, trees, and networks.
MATH 223
MATH 223 has 3 hr.; 3 cr.
MATH 224
MATH 224 has 3 hr.; 3 cr.
MATH 231: Linear Algebra
MATH 231 introduces linear algebra with emphasis on techniques and applications. Topics to be covered include solutions of systems of linear equations, vector spaces, bases and dimension, linear transformations, matrix algebra, determinants, eigenvalues, and inner products. Not open to students who are enrolled in or who have completed MATH 237.
MATH 232: Advanced Linear Algebra
MATH 232 is a second course in linear algebra.
MATH 241: Probability and Statistics
MATH 241 introduces the basic concepts and techniques of probability and statistics with an emphasis on applications. Topics to be covered include the axioms of probability, combinatorial methods, conditional probability, discrete and continuous random variables and distributions, expectations, confidence interval estimations, and tests of hypotheses using the normal, t- and chi-square distributions. Students taking this course may not subsequently receive credit for MATH 114, except by permission of the chair.
MATH 242: Mathematical Statistics
MATH 242 focuses on those methods of mathematical statistics that are most frequently used in the natural and social sciences, as well as actuarial science.
MATH 245: Mathematical Modeling
MATH 245 involves construction, analysis, and assessment of mathematical models as they arise in the physical, biological, and social sciences. Specific topics to be announced in advance.
MATH 247: Optimization
MATH 247 covers methods for handling optimization problems that arise in management, engineering, physical sciences, and social sciences.
MATH 248
MATH 248 has 3 hr.; 3 cr.
MATH 250: Mathematical Programming
MATH 250 introduces a mathematical programming language such as Mathematica, Maple, MATLAB, or Sage. Students will learn algorithmic thinking and apply these ideas to explore problems arising in various areas of mathematics.
MATH 255: Game Theory
MATH 255 covers elements of mathematics of game theory. Foundational material, combinatorial games, zero and non-zero sum games. Two-player matrix games, pure and mixed strategies, pay-offs, equilibrium pairs. This is a proof-based course with an emphasis on examples and applications, especially in economics.
MATH 271
MATH 271 requires MATH 241 (or MATH 611). 1 hr.; 1 cr. Prereq.
MATH 272
MATH 272 has 1 hr.; 1 cr.
MATH 290: Advanced Special Topics
MATH 290's topic is announced in advance. May be repeated for credit if topic is different.
Upper-Level Courses
MATH 301: Abstract Algebra I
MATH 301 delves into the theory of groups, including cyclic and permutation groups, homomorphisms, normal subgroups and quotient groups. Theory of rings, including integral domains and polynomial rings. Additional topics may be discussed. 4 hr.; 4 cr.
MATH 302: Abstract Algebra II
MATH 302 is a continuation of Math 301. Advanced topics in group and ring theory. Fields and field extensions. 3 hr.; 3 cr.
MATH 305: Number Theory
MATH 305 explores prime numbers, the unique factorization property of integers, linear and non-linear Diophantine equations, congruences, modular arithmetic, quadratic reciprocity, contemporary applications in computing and cryptography.
MATH 310: Real Analysis I
MATH 310 offers a rigorous introduction to functions of one real variable. 4 hr.; 4 cr.
MATH 314: Real Analysis II
MATH 314 focuses on mathematical analysis in several variables, including topology of Euclidean space, convergence and continuity of functions, and differentiation and integration of multivariable functions. Topics may include metric spaces, Arzela-Ascoli Theorem, Taylor’s Theorem, and inverse and implicit functions theorems. 4 hr.; 4 cr.
MATH 316: Complex Analysis
MATH 316 covers topics including analytic functions, Cauchy’s Integral Theorem, Taylor’s theorem and Laurent series, the calculus of residues, singularities, meromorphic functions. 3 hr.; 3 cr.
MATH 317: Foundations of Mathematics
MATH 317 focuses on the axiomatic development of the integers, rational numbers, real numbers, and complex numbers. Topics may include sets, relations, and functions; Peano systems; recursive processes; the natural numbers; integers and integral domains; rational numbers and fields; completeness and the real numbers; complex numbers. 3 hr.; 3 cr.
MATH 318: Non-Euclidean Geometry
MATH 318 explores Euclid’s fifth postulate, often referred to as the parallel postulate. Development of the basics of Euclidean geometry with a focus on understanding the role of the fifth postulate. Development and exploration of hyperbolic geometry, a non-Euclidean geometry. 3 hr.; 3 cr.
MATH 320: Topology
MATH 320 covers the basic concepts and fundamental results of point-set topology. The course includes a review of sets and functions, as well as the study of topological spaces including metric spaces, continuous functions, connectedness, compactness, and elementary constructions of topological spaces. 3 hr.; 3 cr.
MATH 334: Graph Theory
MATH 334 delves into families of graphs, graph statistics, graph isomorphism, coloring, cycles, connectivity, planarity, graph algorithms. 3 hr.; 3 cr.
MATH 336: Combinatorics
MATH 336 explores techniques in enumeration. Permutations, combinations, distributions, equivalence classes, principle of inclusion/exclusion, bijective proof, combinatorial proof, generating functions, partitions, Catalan numbers. 3 hr.; 3 cr.
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