# Entry-Level Courses for Freshmen and Sophomores

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

### MATH 1006 - Academic Support for MATH 1106

Spring 2022. 1 credit. S/U grades only.

Students should contact their college for the most up-to-date information regarding if and how credits for this course will count toward graduation, and/or be considered regarding academic standing.

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 1011 - Academic Support for MATH 1110

Fall 2021, Spring 2022. 1 credit. S/U grades only.

Students should contact their college for the most up-to-date information regarding if and how credits for this course will count toward graduation, and/or be considered regarding academic standing.

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 2021, Spring 2022. 1 credit. S/U grades only.

Students should contact their college for the most up-to-date information regarding if and how credits for this course will count toward graduation, and/or be considered regarding academic standing.

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 1021 - Academic Support for MATH 2210

Fall 2021, Spring 2022. 1 credit. S/U grades only.

Reviews material presented in MATH 2210 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 2210 lectures or discussions.

### MATH 1101 - Calculus Preparation

Fall 2021. 1 credit. Letter grades only.

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 1105 - Finite Mathematics for the Life and Social Sciences

Fall 2021. 3 credits. Student option grading.

Prerequisite: three years of high school mathematics, including trigonometry and logarithms.

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 - Modeling with Calculus for the Life Sciences

Spring 2022. 3 credits. Student option grading.

Forbidden Overlap: Due to an overlap in content, students will not receive credit for both MATH 1106 and MATH 1110. For guidance in selecting an appropriate course, please consult First Steps in Math.

Prerequisite: three years of high school mathematics (including trigonometry and logarithms) or a precalculus course (e.g., MATH 1101). No prior knowledge of calculus is required. Students who plan to take more than one semester of calculus should take MATH 1110 rather than MATH 1106.

The goal of this course is to give students a strong basis in some quantitative skills needed in the life and social sciences. There will be an emphasis on modeling, using fundamental concepts from calculus developed in the course, including: derivatives, integrals, and introductory differential equations. Examples from the life sciences are used throughout the course. To give a concrete example, we will study predator-prey populations. We will write down mathematical models that describe the evolution of these populations, analyze both quantitative and qualitative properties to make predictions about the future of these populations, and discuss the assumptions and limitations of the models.

Note that while we will cover the topics of derivatives and integrals, this course has a different, much more applied, focus from courses such as MATH 1110 or a typical high school calculus course.

### MATH 1110 - Calculus I

Summer 2021 (6-week), Fall 2021, Spring 2022. 4 credits. Student option grading.

Note: MATH 1110 will be offered online in Summer 2021.

Forbidden Overlap: Due to an overlap in content, students will not receive credit for both MATH 1110 and MATH 1106. For guidance in selecting an appropriate course, please consult First Steps in Math.

Prerequisite: three years of high school mathematics (including trigonometry and logarithms) or a precalculus course (e.g., MATH 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.

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 2020, Spring 2021. 4 credits. Student option grading.

Forbidden Overlap: Due to an overlap in content, students will not receive credit for both MATH 1120 and MATH 1910. For guidance in selecting an appropriate course, please consult First Steps in Math.

Prerequisite: MATH 1110 with a grade of C or better, excellent performance in MATH 1106, or equivalent AP credit.

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 1300 - Mathematical Explorations

Fall 2021. 3 credits. Student option grading.

Pre-enrollment limited to Arts and Sciences students. Out-of-college students may be able to enroll during the add/drop period.

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 - Strategy, Cooperation, and Conflict

Spring 2022. 3 credits. Student option grading.

We apply mathematical reasoning to problems arising in the social sciences. We discuss game theory and its applications to questions of governing and the analysis of political conflicts. The problem of finding fair election procedures to choose among three or more alternatives is analyzed.

### MATH 1710 - Statistical Theory and Application in the Real World

Fall 2021, Spring 2022. 4 credits. Student option grading.

Forbidden Overlap: Due to an overlap in content, students will receive credit for only one course in the following group: AEM 2100, BTRY 3010, BTRY 6010, ENGRD 2700, HADM 2010, ILRST 2100, ILRST 6100, MATH 1710, PAM 2100, PAM 2101, PSYCH 2500, SOC 3010, STSCI 2100, STSCI 2150, STSCI 2200. In addition, no credit for MATH 1710 if taken after ECON 3130, ECON 3140, ECON 3125, 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 2021 (6-week), Fall 2021, Spring 2022. 4 credits. Student option grading.

Note: MATH 1910 will be offered online in Summer 2021.

Forbidden Overlap: Due to an overlap in content, students will not receive credit for both MATH 1120 and MATH 1910. For guidance in selecting an appropriate course, please consult First Steps in Math.

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

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 2021 (6-week), Fall 2021, Spring 2022. 4 credits. Student option grading.

Note: MATH 1920 will be offered online in Summer 2021.

Forbidden Overlap: Due to an overlap in content, students will receive credit for only one course in the following group: MATH 1920, 2130, 2220, 2240. For guidance in selecting an appropriate course, please consult First Steps in Math.

Prerequisite: MATH 1910 or equivalent AP credit.

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 2022. 4 credits. Student option grading.

Forbidden Overlap: Due to an overlap in content, students will receive credit for only one course in the following group: MATH 1920, 2130, 2220, 2240. For guidance in selecting an appropriate course, please consult First Steps in Math.

Prerequisite: MATH 1120, MATH 1910, or equivalent AP credit. 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 in different coordinate systems; and first- and second-order differential equations with applications. Optional topics may include Green's theorem, the divergence theorem, and systems of differential equations.

### MATH 2210 - Linear Algebra

Fall 2021, Spring 2022. 4 credits. Student option grading.

Forbidden Overlap: Due to an overlap in content, students will receive credit for only one course in the following group: MATH 2210, 2230, 2310, 2940. For guidance in selecting an appropriate course, please consult First Steps in Math.

Prerequisite: two semesters of calculus with high performance, equivalent AP credit, 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. The lectures introduce students to formal proofs. Students are required to produce some proofs in their homework and on exams.

### MATH 2220 - Multivariable Calculus

Fall 2021, Spring 2022. 4 credits. Student option grading.

Forbidden Overlap: Due to an overlap in content, students will receive credit for only one course in the following group: MATH 1920, 2130, 2220, 2240. For guidance in selecting an appropriate course, please consult First Steps in Math.

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 2021. 4 credits. Student option grading.

Forbidden Overlap: Due to an overlap in content, students will receive credit for only one course in the following group: MATH 2210, 2230, 2310, 2940. For guidance in selecting an appropriate course, please consult First Steps in Math.

Prerequisite: two semesters of calculus with grade of A– or better, equivalent AP credit, or permission of instructor. Designed for students who have been extremely successful in their previous calculus courses and for whom the notion of solving very hard problems and writing careful proofs is highly appealing. 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 2022. 4 credits. Student option grading.

Prerequisite: MATH 2230. Designed for students who have been extremely successful in their previous calculus courses and for whom the notion of solving very hard problems and writing careful proofs is highly appealing. 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 2021. 4 credits. Student option grading.

Forbidden Overlap: Due to an overlap in content, students will receive credit for only one course in the following group: MATH 2210, 2230, 2310, 2940. For guidance in selecting an appropriate course, please consult First Steps in Math.

Prerequisite: one semester of college-level calculus, such as MATH 1106 or MATH 1110, or equivalent AP credit. 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)

Fall 2021. 4 credits. Student option grading.

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 2021 (6-week), Fall 2021, Spring 2022. 4 credits. Student option grading.

Note: MATH 2930 will be offered online in Summer 2021.

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); and Fourier series. 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 2021 (6-week), Fall 2021, Spring 2022. 4 credits. Student option grading.

Note: MATH 2940 will be offered online in Summer 2021.

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.