application of cauchy's theorem in real life

General counting methods, pigeonhole principle, inclusion-exclusion principle, generating functions, recurrence relations, summation techniques, partitions, permutations and pattern avoidance, Polya's enumeration, asymptotics, select topics from graph theory. Prerequisite: MAT201 and MAT202 or equivalent. Vector spaces over arbitrary fields, linear transformations, eigenvalues, eigenvectors, inner products, bilinear forms, direct sum decompositions and the Jordan form. Integration of mathematical knowledge and pedagogical techniques to successfully teach Advanced Placement Calculus at the secondary level. Core: Mathematics. Introduction to actuarial science, insurance, and risk management. Analysis of pedagogical methods and materials in early childhood mathematics instruction and assessment. Mathematics topics include, but are not limited to, those taught in grades PreK - 3. © 2021 The Trustees of Princeton University, Equal Opportunity Policy and Nondiscrimination Statement. Theory and application of linear ordinary differential equations: homogeneous and nonhomogeneous linear equations, initial and boundary value problems, exact equations, variation of parameters, Euler equations; solutions of non-linear ordinary differential equations of the first order and second order; power series solutions; system of linear equations. Provides adequate preparation for MAT175. Graded S/U. Download PDF of the Undergraduate Catalog. Seminar for current student interns to discuss topics from the classroom experience and current issues. Engagement in explorations of mathematics to broaden and deepen content knowledge, emphasizing concepts needed to teach secondary mathematics at various levels. The intent is to provide the preparation for the courses in differential geometry and topology. May be repeated for a maximum of 6 units. Supervised original work in pure or applied mathematics. An introduction to the mathematical discipline of analysis, to prepare for higher-level course work in the department. Complex variables: Analytic functions, Cauchy’s integral theorem, Taylor and Laurent series. To cover the elements of calculus on manifolds. May be repeated for a maximum of 6 units,. Prerequisites: MATH 265 or equivalent and MATH 332/ MATH 532 or equivalent. Appropriate technology is integrated throughout. Continuation of MAT103. Hamiltonian and Eulerian graphs, coloring graphs, planar and non-planar graphs, connectivity problems; isomorphic graphs, and advanced topics. Prerequisites: consent of instructor and senior status. Corequisite: MATH 425. Sequences of functions and uniform convergence; Metric spaces, including completeness and compactness. Basic facts about Fourier Series, Fourier Transformations, and applications to the classical partial differential equations will be covered. Two 90-minute classes. Selected further topics may include security protocols, digital cash, elliptic curve cryptography, or quantum cryptography. Core: Advanced Writing Seminar. Prerequisites: MATH 273 and one from MATH 215, MATH 225, MATH 235, or MATH 255; department consent required. Prerequisites: MATH 274; MATH 263 or MATH 267. Sets, logic, induction, functions, relations, sequences, recursion, combinatorics, graphs and trees, matrices with an emphasis on applications in computer science. Core: Mathematics. Intended primarily for students who will use algebraic skills in future mathematics courses. Probability in sample spaces, discrete and continuous random variables, distribution theory, Chebyshev's Theorem, Central Limit Theorem, expected values and moments. This course is suitable both for students preparing to enter the mathematics department and for non-majors interested in exposure to higher mathematics. Other topics include tangent and normal lines, linearization, computing area and rates of change. Prerequisites: MATH 237 Elementary Biostatistics or equivalent and MATH 273 Calculus I or equivalent. Complex number system, analytic functions, Cauchy's integral theorem and integral formula, Taylor and Laurent series, isolated singularities, Cauchy's residue theorem and applications. Prerequisite: MATH 275 (may be taken concurrently). A statistical package such as MINITAB is introduced as a computational tool. Covers the mathematical theory and applications of key financial management concepts and procedures including money growth, force of interest, annuities, perpetuities, amortization, stocks, bonds, yield approximation approaches, term structure of interest rates, swaps, determinants of interest, duration, convexity, and asset matching. Prerequisite: MATH 273. Two 90-minute classes, one computer laboratory. The course is organized in independent two-week modules focusing on particular applications, such as bar codes, CD-players, population models, and space flight. Prerequisites: senior standing and a grade of C or better in MATH 331 and MATH 369; or permission of instructor. Prerequisites: MATH 265 and MATH 331. Analysis of pedagogical methods and materials in elementary school mathematics instruction and assessment. Prerequisites: Admission to Honors College and MATH 273 or Honors Calculus I. Content areas of focus include proportional reasoning, expressions and equations, functions. Core: Mathematics. Topics include Pythagorean triples and sums of squares, unique factorization, Chinese remainder theorem, arithmetic of Gaussian integers, finite fields and cryptography, arithmetic functions, and quadratic reciprocity. The Fourier integral and applications. Utilization of instructional technology to teach mathematics for conceptual understanding, with topics from the areas of algebra, geometry, trigonometry, and calculus. Prerequisite: MATH 331. Four classes. Emphasis on interpretations of results throughout. Prerequisite: qualifying score on Math Placement exam or MATH 119. Graded S/U. Prerequisites: qualifying score on placement test or MATH 95 [DVMT 101] and consent of the department; not open to students completing MATH 115 or higher (except MATH 231 and MATH 237). The second semester in a two-semester precalculus sequence, with a primary focus on trigonometry. Replacing DVMT 101. Prerequisites: consent of instructor and senior status. Techniques of problem solving and the solution of challenging problems involving elementary mathematics, such as probability, number theory, graph theory, and counting. Prerequisite: MATH 274. Content knowledge for teaching elementary school mathematics. Successful completion of Part 1 is required for entry into Part 2. Four classes. Prerequisites: MATH 267 and MATH 275. Team involvement may include literature searches, model definition, collection and analysis of data, and model verification. Prerequisite: qualifying score on Math Placement exam or MATH 100 or higher. Exponential and logarithmic functions, partial derivatives included. 4 contact hours; 3 units. Prerequisite: consent of instructor. Basic concepts and ideas in mathematics are selected to explore the aesthetics and utility of mathematics. Mathematical and comparable computer algebra systems will be used. Prerequisite: MATH 485. Recommended for prospective physics majors and others with a strong interest in applied mathematics. Lab/Class fee will be assessed. ; An edge E or ordered pair is a connection between two nodes u,v that is identified by unique pair(u,v). Fourier series, orthogonal functionspartial differential equations, and boundary value problems. Three classes. An integrated course that covers the material of PHY 103 and MAT 201 with the emphasis on applications to engineering. Intended primarily for students in business, economics, psychology, and the social sciences. Prerequisites: MAT100 or equivalent. First semester of calculus. Continuity, uniform continuity, and differentiability of functions. Problems solving strategies will be applied to a variety of challenging problems, related to topics from middle and high school mathematics curricula. Elliptic functions, theta functions, Jacobi's triple product and combinatorics. Proportional reasoning, algebra, and statistics and data analysis with probability concepts through statistical investigations. Not open to those who successfully completed MATH 361 or MATH 467. Prerequisite: MATH 204. Prerequisites: MATH 273 and department consent. Prerequisites: MATH 332 or equivalent; and MATH 390 (Exam P can be substituted for MATH 390; contact department for permission to enroll). Prerequisites: ENGL 102 or ENGL 190 or equivalent; MATH 273, MATH 274, and MATH 265; either SEMS 230 or SCED 305 (may be taken concurrently); MATH 267 is recommended. Matrix calculations and determinants, vector spaces over the real numbers, linear transformations, eigenvalues, eigenvectors, and inner products with emphasis on applications. Prerequisite: MATH 275 and MATH 265. The emphasis will be on learning to think independently and creatively in the mathematical setting. An introductory course for students with mathematics and computing backgrounds emphasizing statistical ideas and techniques. Topics include the fundamental theorem of finitely generated abelian groups, Sylow theorems, group actions, and the representation theory of finite groups, rings and modules. Lab/Class fee will be assessed. Four classes. Functions of several variables including derivatives and differentiability, multivariable integrals and Fubini’s theorem, null sets and Riemann integrability. Graded S/U. Core: Mathematics. The theory of functions of one complex variable, covering power series expansions, residues, contour integration, and conformal mapping. A rigorous course in linear algebra with an emphasis on proof rather than applications. Functions, limits, and continuity; differentiation of algebraic and trigonometric functions; mean value theorem; differentials; introduction to integration; applications. May be repeated for up to eight units. Descriptive statistics, probability, estimation and sampling, hypothesis testing, regression and correlation, and analysis of variance. Physics topics include: mechanics with applications to fluid mechanics, wave phenomena, and thermodynamics. Four lecture hours and one laboratory hours per week. Prerequisite: MATH 274. Continuation of Multivariable Analysis and Linear Algebra I (MAT 216) from the fall. Vectors in two and three dimensions, differential and integral calculus of functions of several variables. Prerequisites: MATH 330 and MATH 353. Prerequisites: MATH 265 and MATH 275. Geometric vocabulary, relationships, concepts and skills, including properties and classification of two- and three-dimensional shapes; transformations and symmetry; and measurement. One semester survey of the major concepts and computational techniques of calculus including limits, derivatives and integrals. Vectors in the plane and in space, vector functions and motion, surfaces, coordinate systems, functions of two or three variables and their derivatives, maxima and minima and applications, double and triple integrals, vector fields, and Stokes's theorem. Core: Mathematics. Field experience in public school classrooms under the guidance of master teachers and a university supervisor. Prerequisite: MATH 267 or all three of the following: MATH 251, MATH 273, and MATH 265. No credit toward graduation. Simple and multiple regression, least squares estimates, hypothesis testing, confidence intervals and prediction intervals, model building methods and diagnostic checking. Prerequisites: MATH 438; must have attempted two Society of Actuaries exams and passed at least one Society of Actuaries exam. This interdisciplinary course in collaboration with Molecular Biology, Psychology and the Program in Neuroscience is directed toward upper class undergraduate students and first-year graduate students with knowledge of linear algebra and differential equations. These analytic ideas are used to prove the fundamental theorem of algebra, that every non-constant complex polynomial has a root. May be repeated for a maximum of 9 units, provided a different topic is covered. Computer laboratory activities throughout. An overall view of Special Functions via the hypergeometric series. This course deals with topics chosen from recursion theory, proof theory, and model theory. The emphasis is on ideas and mathematical reasoning, not on sophisticated mathematical techniques. Restricted to invited students. Sequences, series, continuity, differentiation, integration and uniform convergence. Angle measures; trigonometric functions and their graphs; trigonometric identities; inverse trigonometric functions and their graphs; algebraic and graphical solutions of trigonometric equations and basic trigonometric inequalities; solving triangles; linear systems in two and three variables with applications to partial fractions; conic sections. Curvatures of curves and surfaces in three dimensional Euclidean space, geodesics, invariants, mappings, and special surfaces. Prerequisites: qualifying score on Math Placement exam, admission to Honors College and MATH 100, or MATH 102 or higher. Emphasis on basic examples and applications of calculus including approximation, differential equations, rates of change and error estimation for students who will take no further calculus. Development of mathematics emphasizing mathematical concepts and contributions and individuals and societies. Not open to students who have successfully taken MATH 255. Topics include the display and analysis of data, conceptual meanings of measures of central tendency and variability, topics in probability, including theoretical approaches and experimental approaches via simulations. Investigation by a team of students under faculty direction of a problem of mathematical and/or computational nature, chosen from proposals submitted by clients in the university or local industry. Prerequisites: MATH 119 or MATH 273 (MATH 273 may be taken concurrently) and department consent. Recommended for prospective physics majors and others with a strong interest in applied mathematics. Best practices for teaching mathematics at the secondary level; analysis and application of methods for planning, conducting, and reflecting on mathematics instruction and assessment. Not open to those who successfully completed MATH 103 or MATH 106. Graded S/U. Introduction to limits and derivatives as preparation for further courses in calculus. Investigation by a team of students under faculty direction of a problem of mathematical and/or computational nature, chosen from proposals submitted by clients in the university or local industry. Mathematical theory, computation and practical applications of financial derivatives in managing financial risk. Specific technologies for study will be chosen based on current use in school settings, and may include calculators, computers, mathematics software and apps, and digital fabrication tools or other makerspace technology. Descriptive statistics, estimation techniques, hypothesis testing, analysis of enumerative data, one-way analysis of variance, and simple linear regression and correlation analysis. Prerequisite: MATH 438. Graded S/U. Not open to mathematics majors or minors. Not open to those who have successfully completed MATH 119. The concept of function, exponential, logarithmic, circular and trigonometric functions, systems of linear equations, vectors in two space, lines, conic sections and polar coordinates. Prerequisites: MATH 265, MATH 274, and COSC 236. Prerequisite: 104 or equivalent. Will provide students with a thorough and rigorous treatment of the following topics in number theory and connections to algebra: factors and multiples; prime numbers and the Fundamental Theorem of Arithmetic; divisibility tests; integers; growing patterns; arithmetic and geometric sequences; functions (linear, quadratic, and exponential); expressions and equations; and additional connections between other branches of mathematics and algebra as time permits. A graph is a data structure that is defined by two components : A node or a vertex.

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