Lower-Level Courses for Freshmen and Sophomores

Please consult First Steps in Math for assistance in selecting an appropriate course.

MATH 1006 - Academic Support for MATH 1106

Spring 2014. 1 credit.

Credit may be used toward good academic standing for students in Architecture, Art, and Planning, Engineering, Hotel Administration, and Human Ecology but not for students in Agriculture and Life Sciences, Arts and Sciences, and Industrial and Labor Relations. Does not count toward graduation.

Reviews material presented in MATH 1106 lectures, provides problem-solving techniques and tips as well as prelim review. Provides further instruction for students who need reinforcement. Not a substitute for attending MATH 1106 lectures or discussions.

MATH 1009 - Precalculus Mathematics

Summer 2013 (6-week). 3 credits.

Does not count toward graduation.

Designed to prepare students for MATH 1110. Reviews algebra, trigonometry, logarithms, and exponentials.

MATH 1011 - Academic Support for MATH 1110

Fall 2013, Spring 2014. 1 credit.

Reviews material presented in MATH 1110 lectures, provides problem-solving techniques and tips as well as prelim review. Provides further instruction for students who need reinforcement. Not a substitute for attending MATH 1110 lectures.

MATH 1012 - Academic Support for MATH 1120

Fall 2013, Spring 2014. 1 credit.

Reviews material presented in MATH 1120 lectures, provides problem-solving techniques and tips as well as prelim review. Provides further instruction for students who need reinforcement. Not a substitute for attending MATH 1120 lectures or discussions.

MATH 1101 - Calculus Preparation

Fall 2013, Spring 2014. 1 credit.

Introduces topics in calculus: limits, rates of change, definition of and techniques for finding derivatives, relative and absolute extrema, and applications. The calculus content of the course is similar to 1/3 of the content covered in MATH 1106 and MATH 1110. In addition, the course includes a variety of topics of algebra, with emphasis on the development of linear, power, exponential, logarithmic, and trigonometric functions. Because of the strong emphasis on graphing, students will have a better understanding of asymptotic behavior of these functions.

MATH 1102 - Introduction to Statistical Methods

Fall 2013. 1 credit.

Introduces topics in probability and statistics: descriptive statistics, linear regression, probability laws and distributions — similar to 1/3 of the content covered in applied, introductory-level statistics courses and MATH 1105. In addition, the course includes a variety of topics of algebra, with emphasis on the development of linear, power, exponential, and logarithmic functions and their applications to curve fitting.

MATH 1105 - Finite Mathematics for the Life and Social Sciences

Fall 2013. 3 credits.

Prerequisite: three years of high school mathematics, including trigonometry and logarithms, or knowledge of topics in MATH 1102.

Introduction to linear algebra, probability, and Markov chains that develops the parts of the theory most relevant for applications. Specific topics include: equations of lines, the method of least squares, solutions of linear systems, matrices; basic concepts of probability, permutations, combinations, binomial distribution, mean and variance, and the normal approximation to the binomial distribution. Examples from biology and the social sciences are used.

MATH 1106 - Calculus for the Life and Social Sciences

Spring 2014. 3 credits.

Forbidden Overlap: Students may not receive credit for both MATH 1106 and MATH 1110.

Prerequisite: three years of high school mathematics (including trigonometry and logarithms) or a precalculus course (e.g., MATH 1009 or 1101). Students who plan to take more than one semester of calculus should take MATH 1110 rather than MATH 1106.

Introduction to differential and integral calculus, partial derivatives, elementary differential equations. Examples from biology and the social sciences are used.

MATH 1110 - Calculus I

Summer 2013 (6-week), Fall 2013, Spring 2014. 4 credits.

Forbidden Overlap: Students may not receive credit for both MATH 1110 and MATH 1106.

Prerequisite: three years of high school mathematics (including trigonometry and logarithms) or a precalculus course (e.g., MATH 1009 or 1101). MATH 1110 can serve as a one-semester introduction to calculus or as part of a two-semester sequence in which it is followed by MATH 1120 or MATH 1220.

Topics include functions and graphs, limits and continuity, differentiation and integration of algebraic, trigonometric, inverse trig, logarithmic, and exponential functions; applications of differentiation, including graphing, max-min problems, tangent line approximation, implicit differentiation, and applications to the sciences; the mean value theorem; and antiderivatives, definite and indefinite integrals, the fundamental theorem of calculus, substitution in integration, the area under a curve.

MATH 1120 - Calculus II

Fall 2013, Spring 2014. 4 credits.

Forbidden Overlap: Students will receive credit for only one course among MATH 1120, 1220, and 1910.

Prerequisite: MATH 1110 with a grade of C or better or excellent performance in MATH 1106. Those who do well in MATH 1110 and expect to major in mathematics or a strongly mathematics-related field should take MATH 1220 instead of 1120.

Focuses on integration: applications, including volumes and arc length; techniques of integration, approximate integration with error estimates, improper integrals, differential equations (separation of variables, initial conditions, systems, some applications). Also covers infinite sequences and series: definition and tests for convergence, power series, Taylor series with remainder, and parametric equations.

MATH 1220 - Honors Calculus II

Fall 2013. 4 credits.

Forbidden Overlap: Students will receive credit for only one course among MATH 1120, 1220, and 1910.

Prerequisite: one semester of calculus with high performance or permission of department. Takes a more theoretical approach to calculus than MATH 1120. Students planning to continue with MATH 2130 are advised to take 1120 instead of this course.

Topics include differentiation and integration of elementary transcendental functions, techniques of integration, applications, polar coordinates, infinite series, and complex numbers, as well as an introduction to proving theorems.

MATH 1300 - [Mathematical Explorations]

Not offered every year. 3 credits.

For students who wish to experience how mathematical ideas naturally evolve. The course emphasizes ideas and imagination rather than techniques and calculations. Homework involves students in actively investigating mathematical ideas. Topics vary depending on the instructor. Some assessment through writing assignments.

MATH 1340 - Mathematics and Politics

Spring 2014. 3 credits.

We apply mathematical reasoning to some problems arising in the social sciences. We discuss game theory and its applications to political and historical conflicts. Power indices are introduced and used to analyze some political institutions. The problem of finding a fair election procedure to choose among three or more alternatives is analyzed.

MATH 1350 - The Art of Secret Writing

Summer 2013 (6-week), Fall 2013. 3 credits.

Prerequisite: three years of high school mathematics.

Examines classical and modern methods of message encryption, decryption, and cryptoanalysis. Mathematical tools are developed to describe these methods (modular arithmetic, probability, matrix arithmetic, number theory), and some of the fascinating history of the methods and people involved is presented.

MATH 1600 - Totally Awesome Mathematics

Spring 2014. 2 credits.

Prerequisite: one semester calculus. (AP credit is sufficient.)

Mathematics is a broad and varied field that extends far beyond calculus and the high school curriculum. This course will introduce exciting mathematical topics to stretch your imagination and give you a feel for the great variety of problems that mathematicians study. Each week a different lecturer will present a new topic and fun problems for discussion. Topics will vary from year to year, but may include the following: encryption and number theory, non-Euclidean geometry, knots and surfaces, combinatorics of polyhedra, the Heisenberg Uncertainty Principle and signal processing, unsolvable problems and noncomputable functions, card shuffling and probability, symmetry and solutions of polynomial equations.

MATH 1710 - Statistical Theory and Application in the Real World

Fall 2013, Spring 2014. 4 credits.

Forbidden Overlap: No credit if taken after ECON 3130 (formerly 3190), ECON 3140 (formerly 3200), ECON 3125 (formerly 3210), MATH 4720, or any other upper-level course focusing on the statistical sciences (e.g., those counting toward the statistics concentration for the math major).

Prerequisite: high school mathematics. No previous familiarity with computers presumed.

Introductory statistics course discussing techniques for analyzing data occurring in the real world and the mathematical and philosophical justification for these techniques. Topics include population and sample distributions, central limit theorem, statistical theories of point estimation, confidence intervals, testing hypotheses, the linear model, and the least squares estimator. The course concludes with a discussion of tests and estimates for regression and analysis of variance (if time permits). The computer is used to demonstrate some aspects of the theory, such as sampling distributions and the Central Limit Theorem. In the lab portion of the course, students learn and use computer-based methods for implementing the statistical methodology presented in the lectures.

MATH 1910 - Calculus For Engineers

Summer 2013 (6-week), Fall 2013, Spring 2014. 4 credits.

Forbidden Overlap: Students will receive credit for only one course among MATH 1120, 1220, and 1910.

Prerequisite: three years high school mathematics, including trigonometry and logarithms, and at least one course in differential and integral calculus.

Essentially a second course in calculus. Topics include techniques of integration, finding areas and volumes by integration, exponential growth, partial fractions, infinite sequences and series, tests of convergence, and power series.

MATH 1920 - Multivariable Calculus for Engineers

Summer 2013 (8-week), Fall 2013, Spring 2014. 4 credits.

Forbidden Overlap: Students will receive credit for only one course among MATH 1920, 2130, 2220, and 2240.

Prerequisite: MATH 1910.

Introduction to multivariable calculus. Topics include partial derivatives, double and triple integrals, line and surface integrals, vector fields, Green’s theorem, Stokes’ theorem, and the divergence theorem.

MATH 2130 - Calculus III

Spring 2014. 4 credits.

Forbidden Overlap: Students will receive credit for only one course among MATH 1920, 2130, 2220, and 2240.

Prerequisite: MATH 1120, 1220, or 1910. Designed for students who wish to master the basic techniques of multivariable calculus, but whose major will not require a substantial amount of mathematics. Students who plan to major or minor in mathematics or take upper-level math courses should take MATH 1920, 2220, or 2240 rather than MATH 2130.

Topics include vectors and vector-valued functions; multivariable and vector calculus including multiple and line integrals; first- and second-order differential equations with applications; systems of differential equations; and elementary partial differential equations. Optional topics may include Green's theorem, Stokes' theorem, and the divergence theorem .

MATH 2210 - Linear Algebra

Fall 2013, Spring 2014. 4 credits.

Forbidden Overlap: Due to an overlap in content, students will receive credit for only one course among MATH 2210, 2230, 2310, and 2940.

Prerequisite: two semesters of calculus with high performance or permission of department. Recommended for students who plan to major or minor in mathematics or a related field. For a more applied version of this course, see MATH 2310.

Topics include vector algebra, linear transformations, matrices, determinants, orthogonality, eigenvalues, and eigenvectors. Applications are made to linear differential or difference equations.

MATH 2220 - Multivariable Calculus

Fall 2013, Spring 2014. 4 credits.

Forbidden Overlap: Students will receive credit for only one course among MATH 1920, 2130, 2220, and 2240.

Prerequisite: MATH 2210. Recommended for students who plan to major or minor in mathematics or a related field.

Differential and integral calculus of functions in several variables, line and surface integrals as well as the theorems of Green, Stokes and Gauss.

MATH 2230 - Theoretical Linear Algebra and Calculus

Fall 2013. 4 credits.

Forbidden Overlap: Students will receive credit for only one course among MATH 2210, 2230, 2310, and 2940.

Prerequisite: two semesters of calculus with grade of A– or better, or permission of instructor. Designed for students who have been highly successful in their previous calculus courses. MATH 2230-2240 provides an integrated treatment of linear algebra and multivariable calculus at a higher theoretical level than in MATH 2210-2220.

Topics include vectors, matrices, and linear transformations; differential calculus of functions of several variables; inverse and implicit function theorems; quadratic forms, extrema, and manifolds; multiple and iterated integrals.

MATH 2240 - Theoretical Linear Algebra and Calculus

Spring 2014. 4 credits.

Forbidden Overlap: Students will receive credit for only one course among MATH 1920, 2130, 2220, and 2240.

Prerequisite: MATH 2230. Designed for students who have been highly successful in their previous calculus courses. MATH 2230-2240 provides an integrated treatment of linear algebra and multivariable calculus at a higher theoretical level than in MATH 2210-2220.

Topics include vector fields; line integrals; differential forms and exterior derivative; work, flux, and density forms; integration of forms over parametrized domains; and Green's, Stokes', and divergence theorems.

MATH 2310 - Linear Algebra with Applications

Fall 2013, Spring 2014. 3 credits.

Forbidden Overlap: Students will receive credit for only one course among MATH 2210, 2230, 2310, and 2940.

Prerequisite: MATH 1110 or equivalent. Students who plan to major or minor in mathematics or take upper-level math courses should take MATH 2210, 2230, or 2940 rather than MATH 2310.

Introduction to linear algebra for students who wish to focus on the practical applications of the subject. A wide range of applications are discussed and computer software may be used. The main topics are systems of linear equations, matrices, determinants, vector spaces, orthogonality, and eigenvalues. Typical applications are population models, input/output models, least squares, and difference equations.

MATH 2810 - Deductive Logic

(also PHIL 3310)

Spring 2014. 4 credits.

Prerequisite: PHIL 2310 or MATH 2210 or MATH 2230 or explicit permission of instructor.

A mathematical study of the formal languages of propositional and predicate logic, including their syntax, semantics, and deductive systems. Various formal results will be established, most importantly soundness and completeness.

MATH 2930 - Differential Equations for Engineers

Summer 2013 (6-week), Fall 2013, Spring 2014. 4 credits.

Prerequisite: MATH 1920. Taking MATH 2930 and 2940 simultaneously is not recommended.

Introduction to ordinary and partial differential equations. Topics include first order equations (separable, linear, homogeneous, exact); mathematical modeling (e.g., population growth, terminal velocity); qualitative methods (slope fields, phase plots, equilibria and stability); numerical methods; second order equations (method of undetermined coefficients, application to oscillations and resonance, boundary value problems and eigenvalues); Fourier series; and linear systems of ordinary differential equations. A substantial part of this course involves partial differential equations, such as the heat equation, the wave equation, and Laplace's equation. (This part must be present in any outside course being considered for transfer credit to Cornell as a substitute for MATH 2930.)

MATH 2940 - Linear Algebra for Engineers

Summer 2013 (6-week), Fall 2013, Spring 2014. 4 credits.

Forbidden Overlap: Students will receive credit for only one course among MATH 2210, 2230, 2310, and 2940.

Prerequisite: MATH 1920. Taking MATH 2930 and 2940 simultaneously is not recommended.

Linear algebra and its applications. Topics include matrices, determinants, vector spaces, eigenvalues and eigenvectors, orthogonality and inner product spaces; applications include brief introductions to difference equations, Markov chains, and systems of linear ordinary differential equations. May include computer use in solving problems.