Yeshiva College Syllabi -- 2021 - 2022 courses (past versions for reference ONLY) -- MAT (Mathematics)

Permanent URI for this collectionhttps://hdl.handle.net/20.500.12202/7011

Syllabi are provided for general information about course scope and content. Syllabi are subject to change.

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Course syllabus: MAT 2462: Mathematical Statistics
(2021-09) Roldan, Pablo; 0000-0003-0034-2863
This course focuses on the theory underlying statistical techniques employed in almost every phase of life: Surveys are designed to collect early returns on election day and forecast the outcome of an election. Consumers are sampled to provide information for predicting product preferences. Research physicians conduct experiments to determine the effect of various drugs and controlled environmental conditions on humans in order to infer the appropriate treatment for various illnesses. Engineers sample a product quality characteristic and various controllable process variables to identify key variables related to product quality. Newly manufactured electronic devices are sampled before shipping to decide whether to ship or hold individual lots. Economists observe various indices of economic health over a period of time and use the information to forecast the condition of the economy in the future. (For course objectives, see below.)
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MAT 1412: Calculus I
(2016-01) Li, Yan
First semester: limits, continuity, derivatives; applications to graphing, maxima and minima, and related rates; mean value theorem; integration, fundamental theorem of the calculus, integration by substitution. Second semester: applications of integration in geometry and physics; methods of integration; improper integrals; indeterminate forms; numerical integration; sequences, power series and Taylor series, polar coordinates; parametric equations. (lecture: 3 hours; recitation: 2 hours) 0.000 TO 4.000 Credit hours
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MAT 2461: Probability Theory
(2021-01) Belbruno, Edward
Course objectives: Basic concepts of probability. Single and multiple random variables, distributions. Theory and applications.
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MAT 2462: Mathematical Statistics
(Yeshiva College, Yeshiva University, 2022-08) Roldan, Pablo; 0000-0003-0034-2863
DESCRIPTION: This course focuses in the theory underlying statistical techniques employed in almost every phase of life: Surveys are designed to collect early returns on election day and forecast the outcome of an election. Consumers are sampled to provide information for predicting product preferences. Research physicians conduct experiments to determine the effect of various drugs and controlled environmental conditions on humans in order to infer the appropriate treatment for various illnesses. Engineers sample a product quality characteristic and various controllable process variables to identify key variables related to product quality. Newly manufactured electronic devices are sampled before shipping to decide whether to ship or hold individual lots. Economists observe various indices of economic health over a period of time and use the information to forecast the condition of the economy in the future.¶ COURSE OUTCOMES:  Students will be able to utilize statistical techniques for addressing quantitative, data-based problems in fields such as biological and social sciences, engineering and technology, business and finance, law, and health and education.  Students will learn the basics of statistical modeling and its limitations  Students will be able to interpret and communicate the results of a statistical analysis  Students will be able to analyze data using statistical computing tools and software
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MAT/COM 1504: Discrete Structures
(2019-01) Roldan, Pablo; 0000-0003-0034-2863
Prerequisite Three years of high school mathematics (exposure to proofs at an informal level, real numbers, integers, rationals, complex numbers, vectors, functions, divisibility, primes, factoring) and an interest in theoretical mathematics. Description The course will introduce students to a variety of topics in higher mathematics that are “discrete” in the sense that they are not dependent on limits and approximation. Discrete mathematics is useful in proving the correctness and deriving the complexity of algorithms and data structures. The subject coverage spans the following core subjects: logic and proofs; sets, functions, sequences, sums, and matrices; number theory; induction; counting; relations. On completion of this course, students will master the fundamentals of discrete mathematics. In subsequent courses, they will apply the basic methods of discrete mathematics to Computer Science (design and analysis of algorithms, computability theory, computer systems, etc.).
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MAT1410: Fundamentals of Calculus
(2021-09) Tong, Bo
This introductory Calculus course is designed for students majoring in biology, pre-health sciences, or any other major except mathematics/computer science/physics/engineering/chemistry. This course provides the fundamental concepts of calculus in the context of applications to the health, life and social sciences, and beyond. Course 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. These knowledge and skills are essential to today's life science workforce and researchers. Students are expected to have pre-calculus skills - high school algebra and trigonometry and must pass the online placement test before the semester.
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MAT1412: Calculus I
(Yeshiva College, Yeshiva University, 2022-08) Li, Yan
First semester: limits, continuity, derivatives; applications to graphing, maxima and minima, and related rates; mean value theorem; integration, fundamental theorem of the calculus, integration by substitution. Second semester: applications of integration in geometry and physics; methods of integration; improper integrals; indeterminate forms; numerical integration; sequences, power series and Taylor series, polar coordinates; parametric equations. (lecture: 3 hours; recitation: 2 hours) 0.000 TO 4.000 Credit hours
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MAT1413: Calculus II
(2020-01) Chen, Wenxiong
First semester: limits, continuity, derivatives; applications to graphing, maxima and minima, and related rates; mean value theorem; integration, fundamental theorem of the calculus, integration by substitution. Second semester: applications of integration in geometry and physics; methods of integration; improper integrals; indeterminate forms; numerical integration; sequences, power series and Taylor series, polar coordinates; parametric equations. (lecture: 3 hours; recitation: 2 hours)
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MAT1413: Problem Seminar
(Yeshiva College, Yeshiva University, 2022-08) Chen, Wenxiong; 0000-0001-8484-5307
First semester: limits, continuity, derivatives; applications to graphing, maxima and minima, and related rates; mean value theorem; integration, fundamental theorem of the calculus, integration by substitution. Second semester: applications of integration in geometry and physics; methods of integration; improper integrals; indeterminate forms; numerical integration; sequences, power series and Taylor series, polar coordinates; parametric equations. (lecture: 3 hours; recitation: 2 hours) 0.000 TO 4.000 Credit hours
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MAT1504: Discrete Structures
(Yeshiva College, Yeshiva University, 2022-08) Belbruno, Edward
Learn the process of analyzing and solving mathematics problems both applied and theoretical.
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MAT1510: Multivariable Calculus
(Yeshiva College, Yeshiva University, 2022-08) Belbruno, Edward; 0000-0002-4241-7336
Vectors, vector functions and curves; functions of several variables, partial derivatives; multiple integrals, Jacobians; vector fields, line and surface integrals; theorems of Green, Gauss, and Stokes. Limits and continuity in Euclidean spaces; partial derivatives, gradient, and chain rule; maxima and minimal with constraints; multiple integrals, cylindrical and spherical coordinates; vector calculus. Prerequisite: MAT 1413 4.000 Credit hours
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MAT1520-1521: Advanced Calculus I and II
(2020-09) Marini, Antonella
Real numbers, limits, intrinsic properties of continuous functions, differentiability and integrability, uniform convergence, implicit and inverse function theorems, point-set topology, metric spaces, curves and surfaces.
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MAT1520-1521: Advanced Calculus I And II
(Yeshiva College, Yeshiva University, 2022-08) Marini, Antonella
Real numbers, limits, intrinsic properties of continuous functions, differentiability and integrability, uniform convergence, implicit and inverse function theorems, point-set topology, metric spaces, curves and surfaces.function theorem. Prerequisite: MAT 1510 3.000 Credit hours
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MAT2105: Linear Algebra
(2021-01) Musser, Maxwell
Systems of linear equations, Gaussian elimination, matrices, matrix algebra; vector spaces, linear transformations, similarity; inner product spaces; determinants; eigen-values and eigenvectors, diagonalization; quadratic forms; canonical forms; complex vector spaces, spectral theory; applications. Prerequisite: MAT 1412
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MAT2105: Linear Algebra
(Yeshiva College, Yeshiva University, 2022-08) Musser, Maxwell
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; complex vector spaces, spectral theory; applications. Prerequisite: MAT 1412 3.000 Credit hours
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MAT2461: Probability Theory
(Yeshiva College, Yeshiva University, 2022-08) Belbruno, Edward; 0000-0002-4241-7336
Probability 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
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MAT2601: Differential Equations
(2020-09) Marini, Antonella
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.
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MATH1510: Multivariable Calculus
(2020-09) Belbruno, Edward
Vectors, vector functions and curves; functions of several variables, partial derivatives; multiple integrals, Jacobians; vector fields, line and surface integrals; theorems of Green, Gauss, and Stokes.
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STA2021: Introduction to Statistics
(2020-09) Malka, Ariel
Course Description: This course introduces students to applied statistics for the social sciences. Course content includes the basic concepts and terminology of statistics, the display of data, re search designs in social science, the basics of survey research methods, central tendency and variability, the basic logic of inferential statistics, t-tests (one - sample, independent means, and matched samples)samples), correlation, regression, analysis of variance, interval estimation for means and other statistics, power and decision errors, and brief coverage of non -parametric statistics.