An Introduction to Mathematical Reasoning: Numbers, Sets and Functions
by Peter J. Eccles
from Cambridge University Press
This book eases students into the rigors of university mathematics. The emphasis is on understanding and constructing proofs and writing clear mathematics. The author achieves this by exploring set theory, combinatorics, and number theory, topics that include many fundamental ideas and may not be a part of a young mathematician's toolkit. This material illustrates how familiar ideas can be formulated rigorously, provides examples demonstrating a wide range of basic methods of proof, and includes some of the all-time-great classic proofs. The book presents mathematics as a continually developing subject. Material meeting the needs of readers from a wide range of backgrounds is included. The over 250 problems include questions to interest and challenge the most able student but also plenty of routine exercises to help familiarize the reader with the basic ideas.
The purpose of this book is to introduce the basic ideas of mathematical proof to students embarking on university mathematics. The emphasis is on helping the reader in understanding and constructing proofs and writing clear mathematics. Over 250 problems include questions to interest and challenge the most able student but also plenty of routine exercises to help familiarize the reader with the basic ideas.
Schaum's Outline of Set Theory and Related Topics
by Seymour Lipschutz
from McGraw-Hill
Confusing Textbooks? Missed Lectures? Not Enough Time?
Fortunately for you, there's Schaum's Outlines. More than 40 million students have trusted Schaum's to help them succeed in the classroom and on exams. Schaum's is the key to faster learning and higher grades in every subject. Each Outline presents all the essential course information in an easy-to-follow, topic-by-topic format. You also get hundreds of examples, solved problems, and practice exercises to test your skills.
This Schaum's Outline gives you
- Practice problems with full explanations that reinforce knowledge
- Coverage of the most up-to-date developments in your course field
- In-depth review of practices and applications
Fully compatible with your classroom text, Schaum's highlights all the important facts you need to know. Use Schaum's to shorten your study time-and get your best test scores!
Schaum's Outlines-Problem Solved.
A-Z of Quantitative PCR (IUL Biotechnology, No. 5) (Iul Biotechnology Series)
from International University Line
This book is a comprehensive manual to allow both the novice researcher and the expert to set up and carry out quantitative PCR assays from scratch. However, this book also sets out to explain as many features of qPCR as possible, provide alternative viewpoints, methods, and aims to simulate the researchers into generating, interpreting, and publishing data that are reproducible, reliable, and biologically meaningful
Independent Component Analysis: A Tutorial Introduction (Bradford Books)
by James V. Stone
from The MIT Press
Independent component analysis (ICA) is becoming an increasingly important tool for analyzing large data sets. In essence, ICA separates an observed set of signal mixtures into a set of statistically independent component signals, or source signals. In so doing, this powerful method can extract the relatively small amount of useful information typically found in large data sets. The applications for ICA range from speech processing, brain imaging, and electrical brain signals to telecommunications and stock predictions.
In Independent Component Analysis, Jim Stone presents the essentials of ICA and related techniques (projection pursuit and complexity pursuit) in a tutorial style, using intuitive examples described in simple geometric terms. The treatment fills the need for a basic primer on ICA that can be used by readers of varying levels of mathematical sophistication, including engineers, cognitive scientists, and neuroscientists who need to know the essentials of this evolving method.
An overview establishes the strategy implicit in ICA in terms of its essentially physical underpinnings and describes how ICA is based on the key observations that different physical processes generate outputs that are statistically independent of each other. The book then describes what Stone calls "the mathematical nuts and bolts" of how ICA works. Presenting only essential mathematical proofs, Stone guides the reader through an exploration of the fundamental characteristics of ICA.
Topics covered include the geometry of mixing and unmixing; methods for blind source separation; and applications of ICA, including voice mixtures, EEG, fMRI, and fetal heart monitoring. The appendixes provide a vector matrix tutorial, plus basic demonstration computer code that allows the reader to see how each mathematical method described in the text translates into working Matlab computer code.
Fuzzy-Set Social Science
by Charles C. Ragin
from University Of Chicago Press
Ragin argues that fuzzy sets allow a far richer dialogue between ideas and evidence in social research than previously possible. They let quantitative researchers abandon "homogenizing assumptions" about cases and causes, they extend diversity-oriented research strategies, and they provide a powerful connection between theory and data analysis. Most important, fuzzy sets can be carefully tailored to fit evolving theoretical concepts, sharpening quantitative tools with in-depth knowledge gained through qualitative, case-oriented inquiry. This book will revolutionize research methods not only in sociology, political science, and anthropology but in any field of inquiry dealing with complex patterns of causation.
The Nuts and Bolts of Proofs, Third Edition
by Antonella Cupillari
from Academic Press
The Nuts and Bolts of Proof instructs students on the basic logic of mathematical proofs, showing how and why proofs of mathematical statements work. It provides them with techniques they can use to gain an inside view of the subject, reach other results, remember results more easily, or rederive them if the results are forgotten.A flow chart graphically demonstrates the basic steps in the construction of any proof and numerous examples illustrate the method and detail necessary to prove various kinds of theorems.
* The "List of Symbols" has been extended.
* Set Theory section has been strengthened with more examples and exercises.
* Addition of "A Collection of Proofs"
How to Read and Do Proofs: An Introduction to Mathematical Thought Processes
by Daniel Solow
from Wiley
This book categorizes, identifies and explains the various techniques that are used repeatedly in all proofs and explains how to read proofs that arise in mathematical literature by understanding which techniques are used and how they are applied.
Set Theory and Its Philosophy: A Critical Introduction
by Michael Potter
from Oxford University Press, USA
Michael Potter presents a comprehensive new philosophical introduction to set theory. Anyone wishing to work on the logical foundations of mathematics must understand set theory, which lies at its heart. What makes the book unique is that it interweaves a careful presentation of the technical material with a penetrating philosophical critique. Potter does not merely expound the theory dogmatically but at every stage discusses in detail the reasons that can be offered for believing it to be true. Set Theory and its Philosophy is a key text for philosophy, mathematical logic, and computer science.
Classic Set Theory: For Guided Independent Study (Chapman & Hall Mathematics)
by D.C. Goldrei
from Chapman & Hall/CRC
Designed for undergraduate students of set theory, Classic Set Theory presents a modern perspective of the classic work of Georg Cantor and Richard Dedekin and their immediate successors. This includes: · The definition of the real numbers in terms of rational numbers and ultimately in terms of natural numbers · Defining natural numbers in terms of sets · The potential paradoxes in set theory · The Zermelo-Fraenkel axioms for set theory · The axiom of choice · The arithmetic of ordered sets · Cantor's two sorts of transfinite number - cardinals and ordinals - and the arithmetic of these. The book is designed for students studying on their own, without access to lecturers and other reading, along the lines of the internationally renowned courses produced by the Open University. There are thus a large number of exercises within the main body of the text designed to help students engage with the subject, many of which have full teaching solutions. In addition, there are a number of exercises without answers so students studying under the guidance of a tutor may be assessed. Classic Set Theory gives students sufficient grounding in a rigorous approach to the revolutionary results of set theory as well as pleasure in being able to tackle significant problems that arise from the theory.
Seaweed Soup (MathStart 1)
by Stuart J. Murphy
from HarperTrophy
It's slimy. It's smelly. Its green and it's gooey. It's seaweed soup -- and its Turtle's favorite lunch!
Turtle has made enough seaweed soup for everyone. But it looks awful and smells worse! Nobody wants to even taste it. How can they tell Turtle without hurting his feelings?
As Turtle serves lunch to his reluctant guests, young readers can learn about matching sets (also called one-to-one correspondence) by keeping track of all the different bowls, cups, spoons, and napkins on the table. Lighthearted art and a surprise ending make this a story readers will eat up.
+++
