If P, Then Q

If P, Then Q
Author: David H. Sanford
Publisher: Psychology Press
Total Pages: 312
Release: 2003
Genre: Conditionals (Logic)
ISBN: 9780415283687

Since its publication in 1989, David Sanford's If P Then Q has become one of the most widely respected works in the field of conditionals. This new edition includes three new chapters, thus updating the book to take into account developments in the

A Spiral Workbook for Discrete Mathematics

A Spiral Workbook for Discrete Mathematics
Author: Harris Kwong
Publisher: Open SUNY Textbooks
Total Pages: 298
Release: 2015-11-06
Genre: Mathematics
ISBN: 9781942341161

A Spiral Workbook for Discrete Mathematics covers the standard topics in a sophomore-level course in discrete mathematics: logic, sets, proof techniques, basic number theory, functions,relations, and elementary combinatorics, with an emphasis on motivation. The text explains and claries the unwritten conventions in mathematics, and guides the students through a detailed discussion on how a proof is revised from its draft to a nal polished form. Hands-on exercises help students understand a concept soon after learning it. The text adopts a spiral approach: many topics are revisited multiple times, sometimes from a dierent perspective or at a higher level of complexity, in order to slowly develop the student's problem-solving and writing skills.

Math in Society

Math in Society
Author: David Lippman
Publisher:
Total Pages: 0
Release: 2012-09-07
Genre: Electronic books
ISBN: 9781479276530

Math in Society is a survey of contemporary mathematical topics, appropriate for a college-level topics course for liberal arts major, or as a general quantitative reasoning course.This book is an open textbook; it can be read free online at http://www.opentextbookstore.com/mathinsociety/. Editable versions of the chapters are available as well.

The Psychology of Proof

The Psychology of Proof
Author: Lance J. Rips
Publisher: MIT Press
Total Pages: 465
Release: 2003-01-01
Genre: Psychology
ISBN: 0262517213

Lance Rips describes a unified theory of natural deductive reasoning and fashions a working model of deduction, with strong experimental support, that is capable of playing a central role in mental life. In this provocative book, Lance Rips describes a unified theory of natural deductive reasoning and fashions a working model of deduction, with strong experimental support, that is capable of playing a central role in mental life. Rips argues that certain inference principles are so central to our notion of intelligence and rationality that they deserve serious psychological investigation to determine their role in individuals' beliefs and conjectures. Asserting that cognitive scientists should consider deductive reasoning as a basis for thinking, Rips develops a theory of natural reasoning abilities and shows how it predicts mental successes and failures in a range of cognitive tasks. In parts I and II of the book, Rips builds insights from cognitive psychology, logic, and artificial intelligence into a unified theoretical structure. He defends the idea that deduction depends on the ability to construct mental proofs—actual memory units that link given information to conclusions it warrants. From this base Rips develops a computational model of deduction based on two cognitive skills: the ability to make suppositions or assumptions and the ability to posit sub-goals for conclusions. A wide variety of original experiments support this model, including studies of human subjects evaluating logical arguments as well as following and remembering proofs. Unlike previous theories of mental proof, this one handles names and variables in a general way. This capability enables deduction to play a crucial role in other thought processes, such as classifying and problem solving. In part III, Rips compares the theory to earlier approaches in psychology which confined the study of deduction to a small group of tasks, and examines whether the theory is too rational or too irrational in its mode of thought.

The Little Typer

The Little Typer
Author: Daniel P. Friedman
Publisher: MIT Press
Total Pages: 418
Release: 2018-09-18
Genre: Computers
ISBN: 0262536439

An introduction to dependent types, demonstrating the most beautiful aspects, one step at a time. A program's type describes its behavior. Dependent types are a first-class part of a language, and are much more powerful than other kinds of types; using just one language for types and programs allows program descriptions to be as powerful as the programs they describe. The Little Typer explains dependent types, beginning with a very small language that looks very much like Scheme and extending it to cover both programming with dependent types and using dependent types for mathematical reasoning. Readers should be familiar with the basics of a Lisp-like programming language, as presented in the first four chapters of The Little Schemer. The first five chapters of The Little Typer provide the needed tools to understand dependent types; the remaining chapters use these tools to build a bridge between mathematics and programming. Readers will learn that tools they know from programming—pairs, lists, functions, and recursion—can also capture patterns of reasoning. The Little Typer does not attempt to teach either practical programming skills or a fully rigorous approach to types. Instead, it demonstrates the most beautiful aspects as simply as possible, one step at a time.

Principia Mathematica

Principia Mathematica
Author: Alfred North Whitehead
Publisher:
Total Pages: 688
Release: 1910
Genre: Logic, Symbolic and mathematical
ISBN:

Elements of Logical Reasoning

Elements of Logical Reasoning
Author: Jan von Plato
Publisher: Cambridge University Press
Total Pages: 275
Release: 2014-01-23
Genre: Mathematics
ISBN: 1139867768

Some of our earliest experiences of the conclusive force of an argument come from school mathematics: faced with a mathematical proof, we cannot deny the conclusion once the premises have been accepted. Behind such arguments lies a more general pattern of 'demonstrative arguments' that is studied in the science of logic. Logical reasoning is applied at all levels, from everyday life to advanced sciences, and a remarkable level of complexity is achieved in everyday logical reasoning, even if the principles behind it remain intuitive. Jan von Plato provides an accessible but rigorous introduction to an important aspect of contemporary logic: its deductive machinery. He shows that when the forms of logical reasoning are analysed, it turns out that a limited set of first principles can represent any logical argument. His book will be valuable for students of logic, mathematics and computer science.

Paper Towns

Paper Towns
Author: John Green
Publisher: A&C Black
Total Pages: 321
Release: 2013
Genre: Juvenile Fiction
ISBN: 140884818X

Quentin Jacobson has spent a lifetime loving Margo Roth Spiegelman from afar. So when she cracks open a window and climbs into his life - dressed like a ninja and summoning him for an ingenious campaign of revenge - he follows. After their all-nighter ends, Q arrives at school to discover that Margo has disappeared.

A Comprehensive Treatment of q-Calculus

A Comprehensive Treatment of q-Calculus
Author: Thomas Ernst
Publisher: Springer Science & Business Media
Total Pages: 491
Release: 2012-09-08
Genre: Mathematics
ISBN: 303480430X

To date, the theoretical development of q-calculus has rested on a non-uniform basis. Generally, the bulky Gasper-Rahman notation was used, but the published works on q-calculus looked different depending on where and by whom they were written. This confusion of tongues not only complicated the theoretical development but also contributed to q-calculus remaining a neglected mathematical field. This book overcomes these problems by introducing a new and interesting notation for q-calculus based on logarithms.For instance, q-hypergeometric functions are now visually clear and easy to trace back to their hypergeometric parents. With this new notation it is also easy to see the connection between q-hypergeometric functions and the q-gamma function, something that until now has been overlooked. The book covers many topics on q-calculus, including special functions, combinatorics, and q-difference equations. Apart from a thorough review of the historical development of q-calculus, this book also presents the domains of modern physics for which q-calculus is applicable, such as particle physics and supersymmetry, to name just a few.​