Supplies, together with MTH1010, the high school math background necessary for a student to enroll in MTH1101 ,MTH1106 , or MTH1113. Includes the arithmetic of signed numbers, fractions, decimals, and percents; operations on polynomials; solvi ng simple first degree equations; and laws of exponents. Prereq: Permission of course coordinator.
Supplies, together with MTH1000, the high school background necessary for a student to enroll in MTH1101, | MTH1106, or MTH1113. Includes solving first and second degree equat ions and systems of equations; graphic lines and parabolas; solving equations with algebraic fractions; solving word problem applications. Prereq: Permission of course coordinator.
Examines linear equations and their graphs, and systems of linear equations and linear inequalities in two variables, with application to linear programming. Introduces matrices with application to Markov chains; set theory, techniques of counting; permut ations and combinations and elementary probability.
Designed for students who enjopy working in collaborative groups. Hands-on explorations of real-life situations, developing concepts from algebra, statistics, and linear programming as needed. Problem solving strategies emphasized. A graphing calculator is required for this course; the TI-83 is strongly recommended.
Examines how to solve various kinds of algebraic equations: linear, quadratic, and linear systems in two and three unknowns. Considers applications to word problems such as motion, mixture, and variational problems. Covers the concept of function, graphs, line slopes, and graphs of polynomials. Also discusses some elementary trigonometry and vectors in the plane. Students do not receive credit for this course if they have already received credit for MTH1188 or MTH119 1.
Introduces differential calculus. Examines elementary rules of differentiation with application to graph sketching and to maximum and minimum problems. Discusses exponential and logarithmic functions with application to compound interest, population grow th, and radioactive decay. Students do not receive credit for MTH1107 if they already received credit for MTH1114.
Offers a review and continuation of differential calculus, graphing and differentiation of trigonometric functions; also presents an introduction to integral calculus with application s to geometric problems and differential equations.
Focuses on the analytic, geometric, and numerical properties of linear, exponential, logarithmic, polynomial, and logistic functions. These functions are studied in the context of using them to model a variety of situations in economics and business including simple and compound interest; mortgages, and the present and future value of both one-time payments and multiple payments/withdrawals. A graphing calculator is required for this course.
Studies functions, derivatives, differential of polynomials, exponential functions and logarithmic functions; graphics functions using maximum, minimum, inflection points; and optimization in nonlinear problems; marginal analysis of cost, revenue, profit functions. Emphasizes work problems and applications. A graphing calculator is required for this course; the TI-83 is strongly recommended. Prereq: MTH1113 or equivalent. Students do not receive credit for MTH1114 if they have already received credit for MTH1107.
Assists students in overcoming deficiencies in pre calculus mathematics without loosing ground in the MTH1123 sequence. Reviews high school algebra, introduces trigonometric functions, and covers the material in MTH1123 and MTH1124. Includes lecture and homework review sessions. (Students placed in this course by request or on the basis of their College Board scores and the result of an orientation-week diagnostic test.)
Introduces the differential calculus of one variable, including trigonometric, exponential, and logarithmic functions, together with their graphs. Includes average rates of change, instantaneous rates of change, derivatives and the chain rule. Covers curve sketching, applications of the derivative to problems involving related rates, and maxima and minima.
Introduces integral calculus including areas, volumes, and other applications. Studies integration involving trigonometric, inverse trigonometric , exponential, and logarithmic functions. Prereq: MTH11 23.
Introduces Taylor polynomials and series; studies differential equations and mathematical models. Prereq: MTH1124.
Begins with the fundamentals of differential calculus and proceeds to specific problems encountered in biological research. Studies the formulation of psychological problems in terms of differential equations; solutions of differential equations by method of undetermined coefficients; and application to compartmental problems.
Studies integral calculus; trigonometric functions; solutions of differential equations by separation of variables; and advanced compartmental problems. Introduces pharmaco-kinetics, numerical integration, and Euler's method. Prereq: MT H1133.
Presents functions of several variables, Taylor polynomials, and infinite series. Prereq: MTH1134.
Covers logic, binary arithmetic, basic set theory, Boolean algebra, and logic gates and their close interconnections. Also studies functions, permutations, combinatorics, proof by induction, algorithms, recursion, and recurrence relations. Prereq: MTH1123.
The sequence MTH 1140-2 is equivalent to MTH 1123-5, but geared towards majors in mathematics, physics, chemistry, and computer science. MTH 1140 introduces differential calculus of one variable, including trigonometric, exponential, and logarithmic functions, together with their graphs. Includes average and instantaneous rates of change, derivatives, and the chain rule. Covers applications of the derivative to curve sketching, related rates, and optimization.
Introduces integral calculus including areas, volumes, and other applications. Studies integration involving trigonometric, inverse trigonometric, exponential, and logarithmic functions. Prereq: MTH1140.
Introduces Taylor polynomials and series; studies differential equations and mathematical models. Prereq: MTH1141.
Presents a computer-oriented introduction to statistical methods, with applications to social and life sciences. Examines descriptive statistics, elementary probability, correlation, and regression, and the fundamentals of statistical inference (confidenc e intervals and hypothethis testing) with a minimum of mathematical derivations. Uses a statistical computer package such as MINITAB or SPSS to solve supplementary problems. Equivalent to MTH1103. Prereq: nonmath majors.
Introduces the statistical style of thinking for students without mathematical sophistication or who ordinarily do not like mathematics. Assigns readings from a wide variety of sources. Uses extensive class discussion and homework problems to teach students to use statistics and to critically evaluate the use of statistics by others. Covers descriptive statistics, statistical tests, confidence intervals, regression and sampling. Economics majors do not receive credit for this course if they have alrea dy earned credit for ECN1250 or MSC1201.
Introduces the computer as a tool for mathematical discovery as well as an object of study. Both the mathematical and computer components may vary, but there will always be an emphasis on the nature of mathematical exploration and the solving of challenging problems.
Develops basic algebraic and problem-solving skills in students who these needs and are enrolled in this course rather than the four-credit MTH1191. Together with MTH1189, prepares the student for calculus ( MTH1193). Includes writing equations and relating word problems to equations, plotting linear equations, word problems involving algebraic fractions, algebraic operations, radicals, inequalities, functional notation and the graphing of functi ons. A graphing calculator is required for this course; the TI-85 or 86 is strongly recommended. Students who earn credit for this course may not receive credit for this course may not receive credit for MTH1106 or MTH1191.
Continues MTH1188. Includes functions and graphing, composite functions and inverse functions, logarithmic and exponential functions and equations, trigonometric functions and their graphs, solving trigonometric problems, trigonometric identities, and vectors in two dimensions. A graphing calculator is required for this course; the TI-85 or 86 is strongly recommended. Equivalent to MTH1192.
Examines laws of exponents, factoring, operations with fractional expressions, radical and complex numbers, Pythagorean Theorem and distance formula, linear and quadratic equations and inequalities, and functional notation. Includes graphing of a wide variety of functions and equations, including lines, conic sections, and polynomials. Studies solutions to many types of equations, including linear, quadratic, and polynomial. Also explores many applications of algebra. A graphing calculator is required; either the TI-83 or TI-86 is recommended. Prereq: BSET majors only. Students who earn credit for this course may not receive credit for MTH1106 or MTH1188.
Studies exponential and logarithmic functions, trigonometric functions of angles in degrees and radians, trigonometric identities and equations, right triangles, law of sines and cosines, inverse trigonometric functions, and polar coordinates. Examines complex numbers in trigonometric form, systems of linear and nonlinear equations, binomial theorem, arithmetic and geometric sequences and series. A graphing calculator is required; either the TI-83 or TI-86 is recommended. Equivalent to MTH1189. Prereq: MTH1191 or MTH1107;BSET majors only.
Studies general function operations, theory and evaluation of limits, derivatives of algebraic and trigonometric functions, general rules of differentiation, Rolle's Theorem and Mean Value Theorem. Also covers applications of differentiation including velocity; and accelerations, related rates, maximum, minimum, curve sketching, and approximations by differentials. A graphing calculator is required; either the TI-83 or TI-86 is recommended. (Not equivalent to MTH1123. Prereq: MTH1192 MTH1123 or MTH1108; BSET majors only.
Begins with antidifferentiation and the solution of problems solved by simples differential equations. Examines the Riemann sum and the development of the fundamental theorem with applications to areas, volumes, and rectilinear motion problems. Topics include logarithmic, exponential, and inverse trigonometric functions and their applications. Studies techniques of integration including parts, partial fractions, substitution, and the use of tables, L'Hopital's rule, improper integrals, and geometry of vectors in a plane and space. A graphing calculator is required; either the TI-83 or TI-86 is recommended. (Not equivalent to MTH1124). Prereq: MTH1193 or MTH1120;BSET majors only.
Begins with sketching surfaces in space leading to a study of functions of several variables, partial derivatives, multiple integrals with applications to area and volume. Studies sequences and series to the development of Taylor and Maclaurin series. Introduces differential equations including the solution, with applications, of first-order variables separable, first-order linear, and second-order linear homogeneous. A graphing calculator is required; either the TI-83 or TI-86 is recommended. (Not equivalent to MT H1125).Prereq: MTH1194 or MTH1121;BSET majors only.
Studies measures of central tendency, measures of variability, frequency distributions and the normal curve, percentiles and standard scores, correlation, inferential statistics, differences between means, analysis of variance (ANOVA), and nonparametric tests. Examines various types of differential equations and methods of solution, including first-order homogenous and nonhomogenous linear equations with constant coefficients. Emphasizes applications and numerical methods throughout the entire course. A graphing calculator is required; either the TI-83 or TI-86 is recommended. Prereq: MTH1194 or MTH1121;BSET majors only.
Traces the development of various branches of mathematics from ancient times to the present, with emphasis on the mathematics itself as well as the mathematicians and cultures that produced it . Teaches students to compute in other number systems, to perf orm geometric constructions, and to learn proofs of some important theorems. Prereq: interest in history of mathematics.
Presents an introduction to concepts and techniques of linear programming, game theory, discrete modeling (shortest path, minimum spanning tree). Explores application to economics, social sciences, and other related fields. Prereq: one year of college mathematics.
Covers partial derivatives and multiple integrals, with applications. Prereq: MTH1125.
Studies ordinary differential equations with applications including mechanical vibrations and electrical circuits. Focuses on first-order equations and systems and second-order linear equations studied from various points of view: existence theory, analytic solution techniques (including Laplace transform), and numerical methods. Uses computer labs for visualization and numerical approximation. Prereq: MTH1125.
Studies partial differential equations with applications. Discusses mathematical models, boundary and initial conditions, Fourier series, and solutions to the wave, diffusion, and Laplace equation. Computer labs are used for visualization and numerical approximation. Prereq: MTH1225.
Introduces matrices through Gaussian elimination. Proceeds to vector spaces and linear equations; orthogonality; eigenvalues and eigenvectors. Emphasizes engineering applications such as systems of ordinary differential equations. Prereq: MTH1225.
Covers elements of number theory with an application to public key codes, and elements of group theory with an application to error-detecting and error-correcting codes. Prereq: MTH1137.
Introduces techniques of mathematical proofs, including mathematical induction. Explores various techniques for counting such as permutation and combinations, inclusion-exclusion principle, Polyaenumeration, and the mathematical formulations necessary for these techniques, including elementary group theory and equivalence relations. Prereq: Two courses in calculus.
Presents an experimental study, using simple mathematical models, of chaotic behavior in dynamical systems found in mathematics, science, and computer science. Goals include the development of experimental skills, integration of visual and analytical modes of thought, and an appreciation of issues of problem formulation and representation. Prereq. MTH 1125, MTH 1137, and COM 1201 or equivalent.
Focuses on methods of calculus and vector analysis to study curves, surfaces, and functions of several variables. Studies parametrization of lines and planes, tangents and normal vectors, partial derivatives, maxima and minima problems, linear approximati on, and tangent planes. Some linear algebra. Prereq: MTH1142.
Continues MTH1243. Covers multiple integration, line integrals, and exact differentials; various forms of Stoke's theorem; and more linear algebra. Prereq: MTH1243.
Studies ordinary differential equations with applications . Focuses on first-order equations and systems and second-order linear equations studied from various points of view: existence theory, analytic solution techniques, and numerical methods. Introduces eigenvalues and eigenvectors to study systems of equations. Uses computer labs for visualization and numerical approximation. Prereq: MTH1142 or equivalent.
Studies partial differential equations with applications. Discusses mathematical models, boundary and initial conditions, Fourier series, and solutions to the wave, diffusion, and Laplace equation. Computer labs are used for visualization and numerical approximation. Prereq: MTH1245.
Focuses on vectors and vector spaces, including function spaces, subspaces. Examines lengths, angels, scalar products; volumes, determinants; linear independence and dependence, dimension, linear and affine maps, kernel and image. Studies algorithms: row operations, double triangular form, inversion. Introduces linear maps. Gives particular attention to characteristic polynomials, eigenvalues, and eigenvectors in low dimensions. Prereq: MTH1244 or equiv.
Focuses on detailed study of linear maps. Studies symmetric maps and quadratic forms, isometries, skew-symmetric maps; decomposition of general linear maps using symmetric maps and isometries. Covers polynomials evaluated on linear maps, generalized eigen spaces, Jordan form. As time permits, introduces computational methods, with emphasis both on geometry underlying algorithms and on particular advantages and limitations. Surveys related areas in mathematics in which linear ideas play a role. Prereq: MTH1301 or equiv.
Provides a theory and technique for a rigorous treatment of calculus. Topics vary and may include the construction of the real numbers, continuity and convergence, differentiation and integration, and proofs of selected results such as the inverse and imp licit function theorems. Emphasizes careful proofs throughout. Prereq: MTH1238 and MTH1243, or permission of the instructor.
Continues MTH1311. Focuses on calculus, applying the concepts introduced in MTH1311. Prereq: MTH1311.
Presents examples of groups (symmetry groups, permutation groups, matrix groups, cyclic groups) and their subgroups. Studies finite groups and orders of subgroups; homomorphisms and normal subgroups. Also considers applications to some of the following, d epending on time and interest: geometry, number theory, crystallography, physics, and combinatorics.
Introduces commutative rings, ideals, integral domains, fields, and Galois theory. Studies extension fields, Gaussian integers, and the same topics as time permits. Prereq: MTH1321.
Introduces the elementary methods of analytic number theory. Focuses on divisibility, congruences, arithmetical and multiplicative functions, quadratic reciprocity, and equivalent formulations of the prime number theorem. Prereq: MTH130 1, or permission of the instructor.
Studies the following topics and the shifts in perspective that their development brought about: disputes over the basics for calculus, twentieth-century discoveries in mathematical logic, and the advent of the computer.
Demonstrates the application of mathematics to interesting physical and biological problems. Examines methods chosen from ordinary and partial differential equations, calculus of various, Laplace transforms, singular perturbations, special functions, dime nsional analysis, and other techniques of applied mathematics. Prereq: MTH1246, or permission of instructor.
In practice, computations are never exact. Therefore, the problem of finding efficient methods to calculate sufficiently accurate answers is of fundamental importance. The emphasis of the course is not on recipes for solving problems, proving theorems, o r on writing computer programs. Rather, the practical concerns of efficiency and accuracy are illustrated by studying the following problems: roots of nonlinear equation, simultaneous linear equations, interpolation, and curve-fitting. Prereq: Two years of calculus and one course in computer programming.
Analyzes problems in differential equations, integration, and ordinary differential equations. (Do not require prior knowledge of differential equations; MTH1349 is not a prerequisite.) Emphasis is similar to that of MTH1349. Prer eq: Two years of calculus and one course in computer programming.
Focuses on algebra and geometry of complex numbers; concepts of limit, continuity, and derivative in the complex domain; homomorphic functions, series, contour integration; and applications. Prereq: MTH1243 or equiv.
Continues MTH1351. May include conformal mapping, analytic continuation, Riemann surfaces, the Laplace transform and inverse transform, elliptic functions, and applications. Prereq: MTH1351 .
This course is intended to give students of mathematics the experience of utilizing their skills to study problems that arise in industry and other ``real-world'' settings. It will also provide the opportunity to build on exciting industrial experiences that they may have had (through Co-op or other employment). Prereq. Junior or Senior status and some experience or interest in applied mathematics. This course satisfies the College of Arts & Sciences Experiential Education requirement.
Studies classical Euclidean geometry and symmetry groups of geometric figures by an analytic approach. Teaches how to formulate mathematical propositions precisely and how to construct and understand mathematical proofs Provides a line between classical and modern geometry with the aim of preparing students for further study in group theory and differential geometry. Prereq: Basic linear algebra or permission of the instructor.
Discusses sample spaces; axioms of probability; random variables and their distributions; expectation, moments, and characteristic function; bivariate distributions; jointly Gaussian random variables; stochastic processes, including autocorrelation function and power spectral density; and estimation of the mean and autocorrelation function in the presence of noise. Prereq: MTH1223 and MTH1225 or equiv.
Focuses on probability functions for finite and infinite spaces; conditional probability and independence; discrete and continuous probability distributions for one or more random variables; expectation; moments; binomial, Poisson, and normal distribution s; Law of Large Numbers; and central limit theorem. Prereq: MTH1223 or MTH1244 .
Studies selected topics, including introduction to stochastic processes, with emphasis on Markov chains or random walk. Prereq: MTH1384 or MTH1387 .
Focuses on estimation of parameters, confidence intervals, hypothesis testing, regression, sampling distributions. Prereq: MTH1384 or MTH1387 .
Special sections for honors students of courses MTH1114, | MTH1123, | MTH1125, | MTH1223, | MTH1133, | MTH1134, | MTH11 35, | MTH1140, | MTH1141, and MTH1142 respectively.
Honors equivalent of MTH1163.
Gives highly motivated students the opportunity to explore mathematical situations and theories in depth. Can be used as an opportunity to examine familiar material in fresh ways or to explore new material not offered in formal courses. Provides students strong in mathematics and the related sciences a chance to develop the art and skill needed to work independently and creatively in mathematics. Prereq: Permission of instructor. Students strong in mathematics are permitted to enroll in graduate mathem atics courses.
Emphasizes mathematical problem-solving techniques from a range of areas, including, but not limited to integration, differentiation, number theory, group theory, field theory, combinatorics, linear algebra, differential equations, and mathematical modeli ng. The mathematical model aspect constitutes one third to one half of the course. Analyzes specific realworld models in complete detail, including running and analyzing computer simulations. Requires students to make a number of presentations to the clas s demonstrating specific techniques. Prereq: Permission of instructor.
Same description as MTH1801-MTH1808. Offered for less intensive projects. Prereq: Permission of instructor.
Same description as MTH1801-MTH1808. Offered for less intensive projects. Prereq: Permission of instructor.
For details contact the honors office
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