mathematics a minimal introduction

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Author : Alexandru Buium
ISBN : 9781482216004
Genre : Mathematics
File Size : 53. 68 MB
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Bridging the gap between procedural mathematics that emphasizes calculations and conceptual mathematics that focuses on ideas, Mathematics: A Minimal Introduction presents an undergraduate-level introduction to pure mathematics and basic concepts of logic. The author builds logic and mathematics from scratch using essentially no background except natural language. He also carefully avoids circularities that are often encountered in related books and places special emphasis on separating the language of mathematics from metalanguage and eliminating semantics from set theory. The first part of the text focuses on pre-mathematical logic, including syntax, semantics, and inference. The author develops these topics entirely outside the mathematical paradigm. In the second part, the discussion of mathematics starts with axiomatic set theory and ends with advanced topics, such as the geometry of cubics, real and p-adic analysis, and the quadratic reciprocity law. The final part covers mathematical logic and offers a brief introduction to model theory and incompleteness. Taking a formalist approach to the subject, this text shows students how to reconstruct mathematics from language itself. It helps them understand the mathematical discourse needed to advance in the field.

Mathematics A Discrete Introduction

Author : Edward A. Scheinerman
ISBN : 9780840049421
Genre : Mathematics
File Size : 28. 93 MB
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MATHEMATICS: A DISCRETE INTRODUCTION teaches students the fundamental concepts in discrete mathematics and proof-writing skills. With its clear presentation, the text shows students how to present cases logically beyond this course. All of the material is directly applicable to computer science and engineering, but it is presented from a mathematician's perspective. Students will learn that discrete mathematics is very useful, especially those whose interests lie in computer science and engineering, as well as those who plan to study probability, statistics, operations research, and other areas of applied mathematics. Important Notice: Media content referenced within the product description or the product text may not be available in the ebook version.

An Introduction To The Minimum Performance Objectives For Mathematics Education In Michigan

Author : Michigan Council of Teachers of Mathematics
ISBN : UOM:39015015208708
Genre : Mathematics
File Size : 42. 8 MB
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Introduction To Modern Mathematics

Author : Helena Rasiowa
ISBN : 9781483274720
Genre : Mathematics
File Size : 65. 6 MB
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Introduction to Modern Mathematics focuses on the operations, principles, and methodologies involved in modern mathematics. The monograph first tackles the algebra of sets, natural numbers, and functions. Discussions focus on groups of transformations, composition of functions, an axiomatic approach to natural numbers, intersection of sets, axioms of the algebra of sets, fields of sets, prepositional functions of one variable, and difference of sets. The text then takes a look at generalized unions and intersections of sets, Cartesian products of sets, and equivalence relations. The book ponders on powers of sets, ordered sets, and linearly ordered sets. Topics include isomorphism of linearly ordered sets, dense linear ordering, maximal and minimal elements, quasi-ordering relations, inequalities for cardinal numbers, sets of the power of the continuum, and Cantor's theorem. The manuscript then examines elementary concepts of abstract algebras, functional calculus and its applications in mathematical proofs, and propositional calculus and its applications in mathematical proofs. The publication is a valuable reference for mathematicians and researchers interested in modern mathematics.

An Introduction To Minimal Currents And Parametric Variational Problems

Author : Enrico Bombieri
ISBN : 3718602997
Genre : Mathematics
File Size : 78. 36 MB
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General Dynamical Processes A Mathematical Introduction

Author :
ISBN : 008095586X
Genre : Mathematics
File Size : 90. 45 MB
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In this book, we study theoretical and practical aspects of computing methods for mathematical modelling of nonlinear systems. A number of computing techniques are considered, such as methods of operator approximation with any given accuracy; operator interpolation techniques including a non-Lagrange interpolation; methods of system representation subject to constraints associated with concepts of causality, memory and stationarity; methods of system representation with an accuracy that is the best within a given class of models; methods of covariance matrix estimation; methods for low-rank matrix approximations; hybrid methods based on a combination of iterative procedures and best operator approximation; and methods for information compression and filtering under condition that a filter model should satisfy restrictions associated with causality and different types of memory. As a result, the book represents a blend of new methods in general computational analysis, and specific, but also generic, techniques for study of systems theory ant its particular branches, such as optimal filtering and information compression. - Best operator approximation, - Non-Lagrange interpolation, - Generic Karhunen-Loeve transform - Generalised low-rank matrix approximation - Optimal data compression - Optimal nonlinear filtering

Introduction To Discrete Mathematics With Isetl

Author : William E. Fenton
ISBN : 0387947825
Genre : Computers
File Size : 81. 22 MB
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Intended for first- or second-year undergraduates, this introduction to discrete mathematics covers the usual topics of such a course, but applies constructivist principles that promote - indeed, require - active participation by the student. Working with the programming language ISETL, whose syntax is close to that of standard mathematical language, the student constructs the concepts in her or his mind as a result of constructing them on the computer in the syntax of ISETL. This dramatically different approach allows students to attempt to discover concepts in a "Socratic" dialog with the computer. The discussion avoids the formal "definition-theorem" approach and promotes active involvement by the reader by its questioning style. An instructor using this text can expect a lively class whose students develop a deep conceptual understanding rather than simply manipulative skills. Topics covered in this book include: the propositional calculus, operations on sets, basic counting methods, predicate calculus, relations, graphs, functions, and mathematical induction.

Mathematics In The 21st Century

Author : Pierre Cartier
ISBN : 9783034808590
Genre : Mathematics
File Size : 44. 48 MB
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Numerous well-presented and important papers from the conference are gathered in the proceedings for the purpose of pointing directions for useful future research in diverse areas of mathematics including algebraic geometry, analysis, commutative algebra, complex analysis, discrete mathematics, dynamical systems, number theory and topology. Several papers on computational and applied mathematics such as wavelet analysis, quantum mechanics, piecewise linear modeling, cosmological models of super symmetry, fluid dynamics, interpolation theory, optimization, ergodic theory and games theory are also presented.

Exploring Mathematics

Author : John Meier
ISBN : 9781107128989
Genre : Mathematics
File Size : 22. 44 MB
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Exploring Mathematics gives students experience with doing mathematics - interrogating mathematical claims, exploring definitions, forming conjectures, attempting proofs, and presenting results - and engages them with examples, exercises, and projects that pique their interest. Written with a minimal number of pre-requisites, this text can be used by college students in their first and second years of study, and by independent readers who want an accessible introduction to theoretical mathematics. Core topics include proof techniques, sets, functions, relations, and cardinality, with selected additional topics that provide many possibilities for further exploration. With a problem-based approach to investigating the material, students develop interesting examples and theorems through numerous exercises and projects. In-text exercises, with complete solutions or robust hints included in an appendix, help students explore and master the topics being presented. The end-of-chapter exercises and projects provide students with opportunities to confirm their understanding of core material, learn new concepts, and develop mathematical creativity.

Introduction To Technical Mathematics

Author : Walter W. Leffin
ISBN : 9781478609353
Genre : Mathematics
File Size : 28. 26 MB
Format : PDF
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Designed for a first course in technical mathematics, this comprehensive, easy-to-read text is ideal for students with minimal mathematics training who wish to prepare for further study in technical areas. The newly revised Third Edition builds on the success of the first two editions, featuring a new chapter on using the quadratic formula to solve quadratic equations. Moreover, extra problem sets that feature technical applications have been added to several chapters. Introduction to Technical Mathematics, 3/E has a versatile format that can be used in many instructional settings. Its user-friendly approach includes problem-solving chapters designed to help students apply basic mathematical principles to a multitude of situations. Students also will benefit from the wealth of applications contained in the worked-out examples and problem sets.

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