# Stern College Syllabi -- Spring and Fall 2021-2022 courses --- MATH (Mathematics)

Permanent URI for this collectionhttps://hdl.handle.net/20.500.12202/7171

"Quotation: 'Mathematics is simply an expression of relationships'" by Ken Whytock is licensed under CC BY-NC 2.0

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Item Restricted MATH 1510: Multivariate Calculus(Stern College for Women, Yeshiva University, 2022-09) Dalezman, MichaelThe course is a continuation of Calculus 1 and 2. The objective is to extend the notions of differentiation and integration to vector-valued functions and functions of several variables.Item Restricted MATH 1504: Discrete Structures(Stern College for Women, Yeshiva University, 2022-09) 0000-0002-4241-7336PREREQUISITE: 3 years of High School mathematics COURSE OUTLINE: Boolean algebra, logic, proof methods, sets, functions, relations, mathematical induction, number theory, probability LEARNING OBJECTIVE: Learn the process of analyzing and solving mathematics problems both applied and theoretical.Item Restricted MATH 1412: Calculus I(Stern College for Women, Yeshiva University, 2022-09) Gidea, MarianPREREQUISITE(S) AND COREQUISITE(S): 1. Three years of high school mathematics 2. Pre-Calculus MATH 1160 OR 3. Passing of the Online Math Placement Test with a minimum score of 20/30. Students who have not achieved the minimum score should register for Pre-Calculus, Math 1160. • Exempt from taking the Online Math Placement Test - Students who have earned a score of 4 or 5 on the AP Calculus exam (AB or AC). - Students who have taken college Calculus and have earned a grade of C or above. COURSE DESCRIPTION: Limits, continuity, derivatives; applications to graphing, maxima and minima, and related rates; mean value theorem; integration, fundamental theorem of the calculus, integration by substitution.Item Restricted MATH 1160: Pre-Calculus(Stern College for Women, Yeshiva University, 2022-09) Liu, XingyuCourse Description: ❖ Pre-Calculus: Introduction to Functions including Polynomials, rational functions, exponential function, logarithmic function and trigonometric functions, sequence and series, basic concept of limit in calculus ❖ Students will be expected to learn the general concept of functions and demonstrate an understanding of materials of Pre-Calculus beyond the manipulation of symbols by applying the techniques of Pre-Calculus to practical problems. General Objectives: Student Learning Outcomes: Students will be able to ❖ handle functions ❖ evaluate and graph functions ❖ perform computations and apply strategies for simplifying expressions, functions and equations and inequalities ❖ transform rectangular coordinate to polar coordinate and do basic calculations ❖ Understand the definition of sequence and series ❖ Apply the knowledge of sequence and series to models ❖ Understand vectors in two and three dimensions and do basic computations ❖ Do basic computations in conic section ❖ write detailed solutions using appropriate mathematical language ❖ identify areas in mathematics and other fields where Pre-Calculus is useful ❖ Learn concept of limit ❖ analyze problems from reality by using the techniques of Pre-CalculusItem Restricted MATH 1410: Fundamentals of Calculus(Stern College for Women, Yeshiva University, 2022-01) Dalezman, MichaelThe object of this course is to introduce the students to the concepts of differentiation and integration. The acquisition of computational skills and applications will be stressed.Item Restricted MATH 2105: Linear algebra I(Stern College for Women, Yeshiva University, 2022-01) Nandori, Peter; 0000-0001-8238-6653COURSE DESCRIPTION: In linear algebra, we learn how to solve systems of linear equations efficiently.Systems of linear equations are one of the most important and most commonly applied mathematical models in a big range of applications in engineering, physics, chemistry, economics, etc. Then we discuss the mathematical abstractions starting from linear equations. Topics to be covered include: Systems of linear equations, Gaussian elimination, matrices, matrix algebra; vector spaces, linear transformations, similarity; inner product spaces; determinants; eigenvalues and eigenvectors,diagonalization; quadratic forms; canonical forms; spectral theory; applications ¶ LEARNING Students will learn all basic concepts of linear algebra. Specific learning objectives: 1. Identify systems of linear equations and solve them with multiple methods. 2. Master the basic concepts of matric algebra 3. Compute determinants and understand its applications 4. Study abstract concepts of vector spaces 5. Apply tools of linear algebra in a range of applied mathematical areasItem Restricted MATH 1413NP Calculus II(2021-01) Dalezman, MichaelFirst semester: limits, derivatives, and integrals; continuous and differentiable functions, mean value theorem, chain rule, implicit differentiation. Applications: curve sketching, maxima and minima, related rates, motion, area. Trigonometric, inverse trigonometric, logarithmic and exponential functions. __Second semester: methods of integration, area, moments, volume. Indeterminate forms, improper integrals, sequences and series. Parametric equations, arc length and polar coordinates. Prerequisite(s): three years of high school mathematics and placement by examination or MATH 1160. This course may be taken as a prerequisite. 0.000 TO 5.000 Credit hoursItem Restricted MATH 1410-M Fundamentals of Calculus(2021-01) Lam, Wai-TingThis course is designed for students majoring in biology, pre-health sciences, or any other major except mathematics, computer science, physics, engineering, chemistry, and physical sciences. Topics include functions, limits, derivatives, and integrals, and problem solving methods, including optimization and related rates problems. Emphasis is placed on developing and interpreting models from a variety of disciplines, on analyzing data, and on graphing and numerical computations. (lecture: 3 hours; recitation: 1 hour). Prerequisite(s): Pre-Calculus, high school Algebra and Trigonometry. This course may be taken as a prerequisite. , 4.000 Credit hours Course Description: ❖ Fundamentals of Calculus: Introduction to limits, differentiations and integrations General Objectives: ❖ Students will be expected to learn the general concept of functions and demonstrate an understanding of materials of Fundamentals of Calculus beyond the manipulation of symbols by applying the techniques of Fundamentals of Calculus to practical problems. Student Learning Outcomes: Students will be able to ❖ handle functions ❖ evaluate and graph functions ❖ perform computations and apply strategies for simplifying expressions, functions and equations and inequalities ❖ calculate limits, derivatives, and indefinite integrals ❖ apply the definition of continuity to pure and applied mathematics problems ❖ use limits, derivative and their properties to analyze graphs of various functions of a single variable including transcendental functions ❖ employ the principles of the differential calculus to solve optimization problems and other applications ❖ calculate the area of regions in the plane- Integrations ❖ perform mathematical operations of functions from reality ❖ productively discuss mathematics in a group setting ❖ write detailed solutions using appropriate mathematical language ❖ identify areas in mathematics and other fields where Calculus is useful ❖ generate solutions to unfamiliar problems ❖ analyze problems from reality by using the techniques of CalculusItem Restricted MATH 2601 - K Differential Equations(2021-01) Gidea, MarianTo solve analytically and numerically differential equations; to perform qualitative analysis and understand long term behavior of systems; to apply differential equations to physics, chemistry, population dynamics, and medicine. Classification of differential equations; existence and uniqueness of solutions; initial-value problems, boundary-value problems; power series methods, integral transforms; numerical algorithms and error estimation; topological methods. Prerequisite(s): MAT 1413. This course may be taken as a prerequisite. 3.000 Credit hoursItem Restricted MATH 2105M Linear Algebra I(2021-01) Dalezman, MichaelThe course begins with the concrete and computational subject of systems of linear equations and gradually exposes the students to the more abstract notions of matrices and vector space. Emphasis is put on computations and applications. The nature of the course requires that concepts introduced in one lecture be used in subsequent lectures. Thus it is imperative that students always be up-to-date. To emphasize this point, there mayl be a 3-minute quiz at the beginning of some lectures and/or occasional collection of homework.. Therefore, students should come on time and students who must be absent should familiarize themselves with the material they missed before coming to the next lecture.Item Restricted MATH 1010C Excursions in Mathematics(2021-01) Ben-Ari, EstherEarly on human beings saw the need for counting physical objects and measuring lengths, areas and volumes. In other words, they needed mathematics. This course will focus on understanding the two basic subjects that mathematics deals with numbers and spaces. In particular, we will learn how negative numbers, rational numbers (fractions) and irrational numbers (such as pi and the square root of 2) arise from the simple counting numbers. Also, we will learn how two- and three-dimensional spaces arise from points and lines. In applying mathematics to everyday life, we will be covering geometry, sets, decimals and percentages, the properties of operations on numbers, measurements of length, area, volume and capacity.Item Restricted Excursions in Mathematics - 13940 - MATH 1010 - L(2021-09) Ben-Ari, EstherThis course is intended for non-science majors and Education majors. Several topics will be taught in depth from the following list: Sets of numbers, geometry, elements of probability and statistics, consumer mathematics, linear programming. 0.000 TO 3.000 Credit hoursItem Restricted Fundamentals of Calculus - 14069 - MATH 1410 - L(2021-09) Liu, XingyuThis course is designed for students majoring in biology, pre-health sciences, or any other major except mathematics, computer science, physics, engineering, chemistry, and physical sciences. Topics include functions, limits, derivatives, and integrals, and problem solving methods, including optimization and related rates problems. Emphasis is placed on developing and interpreting models from a variety of disciplines, on analyzing data, and on graphing and numerical computations. (lecture: 3 hours; recitation: 1 hour). Prerequisite(s): Pre-Calculus, high school Algebra and Trigonometry. This course may be taken as a prerequisite. , 4.000 Credit hoursItem Restricted Discrete Structures - 13953 - MATH 1504 - P(2021-09) Roldan Gonzalez, PabloBoolean algebra and predicate calculus; proof methods; sets, functions, and relations; combinatorics; graph theory and algorithms; mathematical induction and recursion; probability and average case analysis of algorithms. Prerequisite(s): three years of high school mathematics. This course may be taken as a prerequisite. 3.000 Credit hoursItem Restricted Advanced Calculus I - 15054 - MATH 1520 - P(2021-09) Marini, AntonellaReal numbers; theorems on limits; continuous, differentiable, and integrable functions; sequences and series of functions; metric space methods, fixed points, existence theorems for differential equations; implicit function theorem. Prerequisite(s): MATH 1413 and permission of the instructor. This course may be taken as a prerequisite. 3.000 Credit hoursItem Restricted Probability Theory - 13636 - MAT 2461 - 241 ; Probability Theory - 14030 - MATH 2461 - N(2021-09) Nandori, PeterProbability spaces; combinatorics; conditional probability; discrete and continuous random variables; examples; density and distribution functions; independence; expectation and variance; moment-generating functions; law of large numbers; central limit theorem; applications. (See STA 2461.) Prerequisite: MAT 1510 0.000 TO 3.000 Credit hours