Fundamentals of University Mathematics

Fundamentals of University Mathematics
Author: Colin McGregor
Publisher: Elsevier
Total Pages: 564
Release: 2010-10-20
Genre: Mathematics
ISBN: 0857092243

The third edition of this popular and effective textbook provides in one volume a unified treatment of topics essential for first year university students studying for degrees in mathematics. Students of computer science, physics and statistics will also find this book a helpful guide to all the basic mathematics they require. It clearly and comprehensively covers much of the material that other textbooks tend to assume, assisting students in the transition to university-level mathematics.Expertly revised and updated, the chapters cover topics such as number systems, set and functions, differential calculus, matrices and integral calculus. Worked examples are provided and chapters conclude with exercises to which answers are given. For students seeking further challenges, problems intersperse the text, for which complete solutions are provided. Modifications in this third edition include a more informal approach to sequence limits and an increase in the number of worked examples, exercises and problems.The third edition of Fundamentals of university mathematics is an essential reference for first year university students in mathematics and related disciplines. It will also be of interest to professionals seeking a useful guide to mathematics at this level and capable pre-university students. - One volume, unified treatment of essential topics - Clearly and comprehensively covers material beyond standard textbooks - Worked examples, challenges and exercises throughout

Fundamentals of Mathematics

Fundamentals of Mathematics
Author: Denny Burzynski
Publisher:
Total Pages: 0
Release: 2008
Genre: Mathematics
ISBN:

Fundamentals of Mathematics is a work text that covers the traditional study in a modern prealgebra course, as well as the topics of estimation, elementary analytic geometry, and introductory algebra. It is intended for students who: have had previous courses in prealgebra wish to meet the prerequisites of higher level courses such as elementary algebra need to review fundamental mathematical concenpts and techniques This text will help the student devlop the insight and intuition necessary to master arithmetic techniques and manipulative skills. It was written with the following main objectives: to provide the student with an understandable and usable source of information to provide the student with the maximum oppurtinity to see that arithmetic concepts and techniques are logically based to instill in the student the understanding and intuitive skills necessary to know how and when to use particular arithmetic concepts in subsequent material cources and nonclassroom situations to give the students the ability to correctly interpret arithmetically obtained results We have tried to meet these objects by presenting material dynamically much the way an instructure might present the material visually in a classroom. (See the development of the concept of addition and subtraction of fractions in section 5.3 for examples) Intuition and understanding are some of the keys to creative thinking, we belive that the material presented in this text will help students realize that mathematics is a creative subject.

Bridging the Gap to University Mathematics

Bridging the Gap to University Mathematics
Author: Edward Hurst
Publisher: Springer Science & Business Media
Total Pages: 347
Release: 2009-01-08
Genre: Mathematics
ISBN: 1848002904

Helps to ease the transition between school/college and university mathematics by (re)introducing readers to a range of topics that they will meet in the first year of a degree course in the mathematical sciences, refreshing their knowledge of basic techniques and focussing on areas that are often perceived as the most challenging. Each chapter starts with a "Test Yourself" section so that readers can monitor their progress and readily identify areas where their understanding is incomplete. A range of exercises, complete with full solutions, makes the book ideal for self-study.

Fundamentals of Mathematical Analysis

Fundamentals of Mathematical Analysis
Author: Adel N. Boules
Publisher: Oxford University Press, USA
Total Pages: 481
Release: 2021-03-09
Genre: Mathematics
ISBN: 0198868782

Fundamentals of Mathematical Analysis explores real and functional analysis with a substantial component on topology. The three leading chapters furnish background information on the real and complex number fields, a concise introduction to set theory, and a rigorous treatment of vector spaces. Fundamentals of Mathematical Analysis is an extensive study of metric spaces, including the core topics of completeness, compactness and function spaces, with a good number of applications. The later chapters consist of an introduction to general topology, a classical treatment of Banach and Hilbert spaces, the elements of operator theory, and a deep account of measure and integration theories. Several courses can be based on the book. This book is suitable for a two-semester course on analysis, and material can be chosen to design one-semester courses on topology or real analysis. It is designed as an accessible classical introduction to the subject and aims to achieve excellent breadth and depth and contains an abundance of examples and exercises. The topics are carefully sequenced, the proofs are detailed, and the writing style is clear and concise. The only prerequisites assumed are a thorough understanding of undergraduate real analysis and linear algebra, and a degree of mathematical maturity.

Fundamentals of Mathematics

Fundamentals of Mathematics
Author: Bernd S. W. Schröder
Publisher: Wiley
Total Pages: 0
Release: 2010-08-16
Genre: Mathematics
ISBN: 9780470551387

An accessible introduction to abstract mathematics with an emphasis on proof writing Addressing the importance of constructing and understanding mathematical proofs, Fundamentals of Mathematics: An Introduction to Proofs, Logic, Sets, and Numbers introduces key concepts from logic and set theory as well as the fundamental definitions of algebra to prepare readers for further study in the field of mathematics. The author supplies a seamless, hands-on presentation of number systems, utilizing key elements of logic and set theory and encouraging readers to abide by the fundamental rule that you are not allowed to use any results that you have not proved yet. The book begins with a focus on the elements of logic used in everyday mathematical language, exposing readers to standard proof methods and Russell's Paradox. Once this foundation is established, subsequent chapters explore more rigorous mathematical exposition that outlines the requisite elements of Zermelo-Fraenkel set theory and constructs the natural numbers and integers as well as rational, real, and complex numbers in a rigorous, yet accessible manner. Abstraction is introduced as a tool, and special focus is dedicated to concrete, accessible applications, such as public key encryption, that are made possible by abstract ideas. The book concludes with a self-contained proof of Abel's Theorem and an investigation of deeper set theory by introducing the Axiom of Choice, ordinal numbers, and cardinal numbers. Throughout each chapter, proofs are written in much detail with explicit indications that emphasize the main ideas and techniques of proof writing. Exercises at varied levels of mathematical development allow readers to test their understanding of the material, and a related Web site features video presentations for each topic, which can be used along with the book or independently for self-study. Classroom-tested to ensure a fluid and accessible presentation, Fundamentals of Mathematics is an excellent book for mathematics courses on proofs, logic, and set theory at the upper-undergraduate level as well as a supplement for transition courses that prepare students for the rigorous mathematical reasoning of advanced calculus, real analysis, and modern algebra. The book is also a suitable reference for professionals in all areas of mathematics education who are interested in mathematical proofs and the foundation upon which all mathematics is built.

Mastering the Fundamentals of Mathematics

Mastering the Fundamentals of Mathematics
Author: James A. Sellers
Publisher:
Total Pages: 128
Release: 2012
Genre: Algebra
ISBN: 9781598038552

This well-rounded approach to the basics of mathematics is a surefire way to strengthen your current knowledge or to gain new skills for more deftly and confidently approaching and dealing with math. Professor Sellers reveals the secrets behind all the key math topics you need to know. In 24 lectures packed with helpful examples, practice problems, and guided walk-throughs, you'll finally grasp the all-important fundamentals of math in a way that truly sticks.

Math Fundamentals for Audio

Math Fundamentals for Audio
Author: Leslie Gaston-Bird
Publisher:
Total Pages: 0
Release: 2020
Genre: Acoustical engineering
ISBN: 9780895798961

"Math Fundamentals for Audio uniquely complements many popular textbooks on the recording arts and audio engineering with its fresh and thorough presentation of essential mathematical concepts. In this handbook Leslie Gaston-Bird applies principles from algebra, geometry, trigonometry, and calculus to concepts such as Ohm's law, delays, impedance, bandwidth, and decibels. This concise book offers a foundation for connecting mathematics with modern software tools for digital audio."--

Fundamentals of Mathematical Logic

Fundamentals of Mathematical Logic
Author: Peter G. Hinman
Publisher: CRC Press
Total Pages: 894
Release: 2018-10-08
Genre: Mathematics
ISBN: 1439864276

This introductory graduate text covers modern mathematical logic from propositional, first-order and infinitary logic and Gödel's Incompleteness Theorems to extensive introductions to set theory, model theory and recursion (computability) theory. Based on the author's more than 35 years of teaching experience, the book develops students' intuition by presenting complex ideas in the simplest context for which they make sense. The book is appropriate for use as a classroom text, for self-study, and as a reference on the state of modern logic.