Geometry of Principal Sheaves: 578 (Mathematics and Its Applications)
Contents:
Students will explore the relevance of mathematical ideas to fields typically perceived as "nonmathematical" e. The Mystery and Majesty of Ordinary Numbers. Problems arising from the arithmetic of ordinary counting numbers have for centuries fascinated both mathematicians and nonmathematicians. This seminar will consider some of these problems both solved and unsolved. This seminar introduces students to the thought process that goes into developing computational models of biological systems. It will also expose students to techniques for simulating and analyzing these models.
The Language of Mathematics: Making the Invisible Visible. This course will consider mathematics to be the science of patterns and will discuss some of the different kinds of patterns that give rise to different branches of mathematics. Students will discuss combinatorics' deep roots in history, its connections with the theory of numbers, and its fundamental role for natural science, as well as various applications, including cryptography and the stock market.
Students will develop the conceptual framework necessary to understand waves of any kind, starting from laboratory observations. Letter grade Same as: A View of the Sea: Why is the Gulf Stream so strong, why does it flow clockwise, and why does it separate from the United States coast at Cape Hatteras? Students will study the circulation of the ocean and its influence on coastal environments by reading the book A View of the Sea by the eminent oceanographer Hank Stommel and by examining satellite and on-site observations.
Colliding Balls and Springs: The Microstructure of How Materials Behave. Students will follow the intellectual journey of the atomic hypothesis from Leucippus and Democritus to the modern era, combining the history, the applications to science, and the mathematics developed to study particles and their interactions. Non-Euclidean Geometry in Nature and History. The seminar will investigate non-Euclidean geometry hyperbolic and spherical from historical, mathematical, and practical perspectives.
The approach will be largely algebraic, in contrast to the traditional axiomatic method. The Mathematics of Climate Change: Is the Earth warming? Predictions are based largely on mathematical models. We shall consider the limitations of models in relation to making predictions. Examples of chaotic behavior will be presented.
Content will vary each semester.
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Honors version available Repeat rules: May be repeated for credit; may be repeated in the same term for different topics; 6 total credits. Provides a one-semester review of the basics of algebra. Basic algebraic expressions, functions, exponents, and logarithms are included, with an emphasis on problem solving. This course should not be taken by those with a suitable score on the achievement test.
Provides an introduction in as nontechnical a setting as possible to the basic concepts of calculus. The course is intended for the nonscience major. Aspects of Finite Mathematics. Introduction to basic concepts of finite mathematics, including topics such as counting methods, finite probability problems, and networks. Aspects of Modern Mathematics. Introduction to mathematical topics of current interest in society and science, such as the mathematics of choice, growth, finance, and shape.
Introduction to Mathematical Modeling. Provides an introduction to the use of mathematics for modeling real-world phenomena in a nontechnical setting. Models use algebraic, graphical, and numerical properties of elementary functions to interpret data. This course is intended for the nonscience major.
Awarded as placement credit based on test scores. Does not fulfill a graduation requirement. Covers the basic mathematical skills needed for learning calculus. Topics are calculating and working with functions and data, introduction to trigonometry, parametric equations, and the conic sections. Calculus for Business and Social Sciences.
An introductory survey of differential and integral calculus with emphasis on techniques and applications of interest for business and the social sciences. Special Topics in Mathematics. An undergraduate seminar course that is designed to be a participatory intellectual adventure on an advanced, emergent, and stimulating topic within a selected discipline in mathematics. This course does not count as credit towards the mathematics major.
Calculus of Functions of One Variable I. Limits, derivatives, and integrals of functions of one variable. Honors version available Requisites: Calculus of the elementary transcendental functions, techniques of integration, indeterminate forms, Taylor's formula, infinite series. Calculus of Functions of Several Variables. Vector algebra, solid analytic geometry, partial derivatives, multiple integrals.
Limits, derivatives, and integrals of functions of one variable, motivated by and applied to discrete-time dynamical systems used to model various biological processes.
Requires knowledge of linear algebra and algebraic structures. Computer-Assisted Mathematical Problem Solving. Linear algebra and its applications. Vector algebra, solid analytic geometry, partial derivatives, multiple integrals. Applications to the life sciences may include muscle physiology, biological fluid dynamics, neurobiology, molecular regulatory networks, and cell biology. Requires knowledge of linear algebra.
Techniques of integration, indeterminate forms, Taylor's series; introduction to linear algebra, motivated by and applied to ordinary differential equations; systems of ordinary differential equations used to model various biological processes. Permission of the instructor. Elective topics in mathematics.
This course has variable content and may be taken multiple times for credit. Undergraduate Seminar in Mathematics. A seminar on a chosen topic in mathematics in which the students participate more actively than in usual courses. May be repeated for credit. Directed Exploration in Mathematics. By permission of the director of undergraduate studies. Experimentation or deeper investigation under the supervision of a faculty member of topics in mathematics that may be, but need not be, connected with an existing course.
No one may receive more than seven semester hours of credit for this course. May be repeated for credit; may be repeated in the same term for different topics; 7 total credits. Revisiting Real Numbers and Algebra. Central to teaching precollege mathematics is the need for an in-depth understanding of real numbers and algebra.
This course explores this content, emphasizing problem solving and mathematical reasoning. This course serves as a transition from computational to more theoretical mathematics. Topics are from the foundations of mathematics: First Course in Differential Equations. Introductory ordinary differential equations, first- and second-order differential equations with applications, higher-order linear equations, systems of first-order linear equations introducing linear algebra as needed.
The book provides a detailed introduction to the theory of connections on principal sheaves in the framework of Abstract Differential Geometry (ADG). This is a. Find great deals for Mathematics and Its Applications: Geometry of Principal Sheaves by Efstathios Vassiliou (, Hardcover). Shop with confidence on .
First Course in Differential Equations Laboratory. Course is computational laboratory component designed to help students visualize ODE solutions in Matlab. Emphasis is on differential equations motivated by applied sciences. Some applied linear algebra will appear as needed for computation and modeling purposes. Undergraduate Reading and Research in Mathematics. Permission of the director of undergraduate studies. This course is intended mainly for students working on honors projects. No one may receive more than three semester hours credit for this course.
Mathematical Methods in Biostatistics. Special mathematical techniques in the theory and methods of biostatistics as related to the life sciences and public health. Includes brief review of calculus, selected topics from intermediate calculus, and introductory matrix theory for applications in biostatistics.
Geometry of Principal Sheaves (Hardcover, 2005 ed.)
Teaching and Learning Mathematics. Study of how people learn and understand mathematics, based on research in mathematics, mathematics education, psychology, and cognitive science. This course is designed to prepare undergraduate mathematics majors to become excellent high school mathematics teachers. It involves field work in both the high school and college environments. An investigation of various ways elementary concepts in mathematics can be developed.
Applications of the mathematics developed will be considered. An examination of high school mathematics from an advanced perspective, including number systems and the behavior of functions and equations. Designed primarily for prospective or practicing high school teachers. A general survey of the history of mathematics with emphasis on elementary mathematics.
Geometry and its applications - PDF Free Download
Some special problems will be treated in depth. The real numbers, continuity and differentiability of functions of one variable, infinite series, integration. Functions of several variables, the derivative as a linear transformation, inverse and implicit function theorems, multiple integration. Functions of a Complex Variable with Applications.
The algebra of complex numbers, elementary functions and their mapping properties, complex limits, power series, analytic functions, contour integrals, Cauchy's theorem and formulae, Laurent series and residue calculus, elementary conformal mapping and boundary value problems, Poisson integral formula for the disk and the half plane.
Linear differential equations, power series solutions, Laplace transforms, numerical methods. Mathematical Methods for the Physical Sciences I. Theory and applications of Laplace transform, Fourier series and transform, Sturm-Liouville problems. Students will be expected to do some numerical calculations on either a programmable calculator or a computer.
This course has an optional computer laboratory component: Students will need a CCI-compatible computing device. Introduction to boundary value problems for the diffusion, Laplace and wave partial differential equations. Bessel functions and Legendre functions. Introduction to complex variables including the calculus of residues.
Elementary Theory of Numbers. Divisibility, Euclidean algorithm, congruences, residue classes, Euler's function, primitive roots, Chinese remainder theorem, quadratic residues, number-theoretic functions, Farey and continued fractions, Gaussian integers. Elements of Modern Algebra.
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- Geometry of principal sheaves [electronic resource] in SearchWorks catalog.
Binary operations, groups, subgroups, cosets, quotient groups, rings, polynomials. Introduction to mathematical theory of probability covering random variables; moments; binomial, Poisson, normal and related distributions; generating functions; sums and sequences of random variables; and statistical applications.
Linear Algebra for Applications. Algebra of matrices with applications: Counting selections, binomial identities, inclusion-exclusion, recurrences, Catalan numbers. Selected topics from algorithmic and structural combinatorics, or from applications to physics and cryptography. Expected dispatch within 7 - 11 working days. Is the information for this product incomplete, wrong or inappropriate? Let us know about it. Does this product have an incorrect or missing image? Send us a new image.
Is this product missing categories? Checkout Your Cart Price. Description Details Customer Reviews L' inj' ' enuit' ' m eme d' un regard neuf celui de la science l'est toujours peut parfois ' 'clairer d' un jour nouveau d' anciens probl' emes. Mallios'sGeometry of Vector Sheaves [62]. Based on sheaf-theoretic methods and sheaf - homology, the presentGeometry of Principal Sheaves embodies the classical theory of connections on principal and vector bundles, and connections on vector sheaves, thus paving the way towards a uni?