https://mklab.gr/ Wed, 29 Jul 2026 08:23:15 +0000 MyBB https://mklab.gr/showthread.php?tid=1338 Sun, 26 Jul 2026 01:41:51 +0300 mklabgr]]> https://mklab.gr/showthread.php?tid=1338 "A=B" by Marko Petkovsek, Herbert Wilf and Doron Zeilberger

Summary

The book details a major breakthrough in computer algebra and discrete mathematics: the complete automation of discovering and proving mathematical identities, particularly hypergeometric and binomial coefficient sums. By replacing complex manual combinatorial proofs with algorithmic, computer-generated methods, the authors demonstrate how software can systematically simplify and verify intricate mathematical equations.

 This hub provides free downloads of the complete book alongside updated software programs, such as EKHAD, that carry out these automated algorithms. It also features supplementary resources including errata sheets, real-world case studies, and materials from university courses built around the text. 

Reviewers consistently praise the work for its engaging, accessible, and tutorial-style exposition, which makes cutting-edge research in automatic theorem proving understandable to undergraduates, computer scientists, and veteran mathematicians alike. Furthermore, the page acts as an interactive platform where readers are encouraged to report software bugs, share interesting write-ups, and contribute new applications of these algorithmic methods.

BOOK]]> "A=B" by Marko Petkovsek, Herbert Wilf and Doron Zeilberger

Summary

The book details a major breakthrough in computer algebra and discrete mathematics: the complete automation of discovering and proving mathematical identities, particularly hypergeometric and binomial coefficient sums. By replacing complex manual combinatorial proofs with algorithmic, computer-generated methods, the authors demonstrate how software can systematically simplify and verify intricate mathematical equations.

 This hub provides free downloads of the complete book alongside updated software programs, such as EKHAD, that carry out these automated algorithms. It also features supplementary resources including errata sheets, real-world case studies, and materials from university courses built around the text. 

Reviewers consistently praise the work for its engaging, accessible, and tutorial-style exposition, which makes cutting-edge research in automatic theorem proving understandable to undergraduates, computer scientists, and veteran mathematicians alike. Furthermore, the page acts as an interactive platform where readers are encouraged to report software bugs, share interesting write-ups, and contribute new applications of these algorithmic methods.

BOOK]]> https://mklab.gr/showthread.php?tid=754 Fri, 26 Jun 2026 18:29:03 +0300 mklabgr]]> https://mklab.gr/showthread.php?tid=754 Patterns 
by Julian F. Fleron

Summary

Discovering the Art of Mathematics: Patterns is an open-source, inquiry-based learning guide designed to help liberal arts students explore mathematics as the ultimate study of structure and design. Rather than relying on traditional rote memorization or heavy algebraic manipulation, authors Julian F. Fleron and Philip K. Hotchkiss invite readers to act as "explorers," uncovering the mathematical frameworks hidden within beautiful Islamic art, the mechanics of Spirographs, and the linguistic history of naming impossibly large numbers like a "millinillitrillion." 

By guiding students through hands-on investigations of geometric stars, discrete calculus, and classic counting riddles, the text transforms math into an accessible, creative playground that fosters problem-solving intuition and deepens appreciation for how order shapes the world around us.

BOOK]]> Patterns 
by Julian F. Fleron

Summary

Discovering the Art of Mathematics: Patterns is an open-source, inquiry-based learning guide designed to help liberal arts students explore mathematics as the ultimate study of structure and design. Rather than relying on traditional rote memorization or heavy algebraic manipulation, authors Julian F. Fleron and Philip K. Hotchkiss invite readers to act as "explorers," uncovering the mathematical frameworks hidden within beautiful Islamic art, the mechanics of Spirographs, and the linguistic history of naming impossibly large numbers like a "millinillitrillion." 

By guiding students through hands-on investigations of geometric stars, discrete calculus, and classic counting riddles, the text transforms math into an accessible, creative playground that fosters problem-solving intuition and deepens appreciation for how order shapes the world around us.

BOOK]]> https://mklab.gr/showthread.php?tid=753 Fri, 26 Jun 2026 18:26:48 +0300 mklabgr]]> https://mklab.gr/showthread.php?tid=753 Truth, Reasoning, Certainty, & Proof 
by Julian F. Fleron

Summary

Truth, Reasoning, Certainty, and Proof is an interactive learning guide that invites you to step away from dry formulas and explore what makes mathematical truth so unique and absolute. By diving into head-scratching paradoxes, optical illusions, and historical shifts in thinking, the book gently challenges how you view certainty before guiding you to build your own actual proofs behind magic tricks, geometric mysteries, and even imaginary numbers. 

It keeps things grounded and human by weaving in playful puzzles like the famous "Knights and Knaves" riddles, ultimately taking you on a journey to the very edge of modern knowledge—where chaos theory, fractals, and Gödel's incompleteness theorems show us the fascinating limits of what we can truly understand.

BOOK]]> Truth, Reasoning, Certainty, & Proof 
by Julian F. Fleron

Summary

Truth, Reasoning, Certainty, and Proof is an interactive learning guide that invites you to step away from dry formulas and explore what makes mathematical truth so unique and absolute. By diving into head-scratching paradoxes, optical illusions, and historical shifts in thinking, the book gently challenges how you view certainty before guiding you to build your own actual proofs behind magic tricks, geometric mysteries, and even imaginary numbers. 

It keeps things grounded and human by weaving in playful puzzles like the famous "Knights and Knaves" riddles, ultimately taking you on a journey to the very edge of modern knowledge—where chaos theory, fractals, and Gödel's incompleteness theorems show us the fascinating limits of what we can truly understand.

BOOK]]> https://mklab.gr/showthread.php?tid=559 Mon, 22 Jun 2026 07:07:09 +0300 mklabgr]]> https://mklab.gr/showthread.php?tid=559 An Introduction to Proofs and the Mathematical Vernacular 
BY Martin V. Day

Summary

An Introduction to Proofs and the Mathematical Vernacular by Martin V. Day is a textbook designed to help students transition from computational mathematics (such as calculus exercises) to the more abstract world of university mathematics, where constructing and understanding proofs is essential. Instead of beginning with formal logic alone, the book introduces proof techniques through concrete examples and gradually develops the language, structure, and reasoning behind mathematical arguments. 

It covers topics such as direct proofs, contradiction, induction, sets, functions, number theory, inequalities, polynomials, determinants, and the role of axioms, while emphasizing how mathematicians think, read, and write proofs. The goal is not just to teach proof formats but to develop mathematical maturity: the ability to recognize ideas behind arguments, communicate precisely, and understand rigorous reasoning across different areas of mathematics. 

BOOK PAGE]]> An Introduction to Proofs and the Mathematical Vernacular 
BY Martin V. Day

Summary

An Introduction to Proofs and the Mathematical Vernacular by Martin V. Day is a textbook designed to help students transition from computational mathematics (such as calculus exercises) to the more abstract world of university mathematics, where constructing and understanding proofs is essential. Instead of beginning with formal logic alone, the book introduces proof techniques through concrete examples and gradually develops the language, structure, and reasoning behind mathematical arguments. 

It covers topics such as direct proofs, contradiction, induction, sets, functions, number theory, inequalities, polynomials, determinants, and the role of axioms, while emphasizing how mathematicians think, read, and write proofs. The goal is not just to teach proof formats but to develop mathematical maturity: the ability to recognize ideas behind arguments, communicate precisely, and understand rigorous reasoning across different areas of mathematics. 

BOOK PAGE]]> https://mklab.gr/showthread.php?tid=558 Mon, 22 Jun 2026 06:57:03 +0300 mklabgr]]> https://mklab.gr/showthread.php?tid=558 PROOF IN MATHEMATICS: AN INTRODUCTION
James Franklin and Albert Daoud

Summary

“Proofs” by Jim (James) Franklin at the University of New South Wales is an introduction to the role and nature of mathematical proofs, explaining why proof is what distinguishes mathematics from experimental sciences. It discusses how mathematicians use logical deduction from axioms and previously established results to achieve certainty, unlike sciences that rely on observation and testing. 
The material introduces the structure of proofs, the difference between examples and rigorous arguments, and gives elementary proof techniques to help students understand how mathematical statements are established. It also highlights the historical importance of proof, from ancient Greek mathematics to modern fields, showing how proofs provide a foundation for mathematical knowledge and reasoning. 

BOOK PAGE]]> PROOF IN MATHEMATICS: AN INTRODUCTION
James Franklin and Albert Daoud

Summary

“Proofs” by Jim (James) Franklin at the University of New South Wales is an introduction to the role and nature of mathematical proofs, explaining why proof is what distinguishes mathematics from experimental sciences. It discusses how mathematicians use logical deduction from axioms and previously established results to achieve certainty, unlike sciences that rely on observation and testing. 
The material introduces the structure of proofs, the difference between examples and rigorous arguments, and gives elementary proof techniques to help students understand how mathematical statements are established. It also highlights the historical importance of proof, from ancient Greek mathematics to modern fields, showing how proofs provide a foundation for mathematical knowledge and reasoning. 

BOOK PAGE]]> https://mklab.gr/showthread.php?tid=334 Sun, 14 Jun 2026 15:18:44 +0300 mklabgr]]> https://mklab.gr/showthread.php?tid=334 What is mathemarics 
by Richard Courand and Herbert Robbins

Summary  What is Mathematics? An Elementary Approach to Ideas and Methods is a classic mathematics book written by Richard Courant and Herbert Robbins, originally published in 1941. It is widely celebrated as an accessible, engaging survey designed to bridge the gap between abstract mathematical concepts and the curious general public.

What_Is_Mathematics(2nd_edition_1996)v2.pdf]BOOK PAGE ]]> What is mathemarics 
by Richard Courand and Herbert Robbins

Summary  What is Mathematics? An Elementary Approach to Ideas and Methods is a classic mathematics book written by Richard Courant and Herbert Robbins, originally published in 1941. It is widely celebrated as an accessible, engaging survey designed to bridge the gap between abstract mathematical concepts and the curious general public.

What_Is_Mathematics(2nd_edition_1996)v2.pdf]BOOK PAGE ]]> https://mklab.gr/showthread.php?tid=278 Wed, 10 Jun 2026 23:31:41 +0300 mklabgr]]> https://mklab.gr/showthread.php?tid=278 A Concise Introduction to Logic
Author(s): Craig DeLancey

Summary

A Concise Introduction to Logic is an introduction to formal logic suitable for undergraduates taking a general education course in logic or critical thinking, and is accessible and useful to any interested in gaining a basic understanding of logic.  This text takes the unique approach of teaching logic through intellectual history; the author uses examples from important and celebrated arguments in philosophy to illustrate logical principles.  The text also includes a basic introduction to findings of advanced logic.  As indicators of where the student could go next with logic, the book closes with an overview of advanced topics, such as the axiomatic method, set theory, Peano arithmetic, and modal logic.  Throughout, the text uses brief, concise chapters that readers will find easy to read and to review.

BOOK PAGE]]> A Concise Introduction to Logic
Author(s): Craig DeLancey

Summary

A Concise Introduction to Logic is an introduction to formal logic suitable for undergraduates taking a general education course in logic or critical thinking, and is accessible and useful to any interested in gaining a basic understanding of logic.  This text takes the unique approach of teaching logic through intellectual history; the author uses examples from important and celebrated arguments in philosophy to illustrate logical principles.  The text also includes a basic introduction to findings of advanced logic.  As indicators of where the student could go next with logic, the book closes with an overview of advanced topics, such as the axiomatic method, set theory, Peano arithmetic, and modal logic.  Throughout, the text uses brief, concise chapters that readers will find easy to read and to review.

BOOK PAGE]]> https://mklab.gr/showthread.php?tid=260 Wed, 10 Jun 2026 04:13:56 +0300 mklabgr]]> https://mklab.gr/showthread.php?tid=260 The Art of Proof: Basic Training For Deeper Mathematics 
 Matthias Beck

Summary 
The Art of Proof: Basic Training For Deeper Mathematics (2010) by Matthias Beck and Ross Geoghegan, which provides a free, searchable PDF version of the book for individual use. Designed as a transition text for students who have completed calculus, the book teaches rigorous proof-writing and logic organically through concrete mathematical concepts rather than in the abstract. 
It is divided equally into two parts—The Discrete (covering integers, induction, modular arithmetic, and algorithms) and The Continuous (covering real/rational numbers, limits, and countability)—and includes short seminar essays on advanced topics like cryptography and group theory. 

Highly praised by reviewers, the textbook successfully bridges the gap between intuitive computation and abstract higher mathematics by balancing deep mathematical rigor with a witty, accessible writing style that even incorporates cartoons and philosophical quotes.

BOOK PAGE]]> The Art of Proof: Basic Training For Deeper Mathematics 
 Matthias Beck

Summary 
The Art of Proof: Basic Training For Deeper Mathematics (2010) by Matthias Beck and Ross Geoghegan, which provides a free, searchable PDF version of the book for individual use. Designed as a transition text for students who have completed calculus, the book teaches rigorous proof-writing and logic organically through concrete mathematical concepts rather than in the abstract. 
It is divided equally into two parts—The Discrete (covering integers, induction, modular arithmetic, and algorithms) and The Continuous (covering real/rational numbers, limits, and countability)—and includes short seminar essays on advanced topics like cryptography and group theory. 

Highly praised by reviewers, the textbook successfully bridges the gap between intuitive computation and abstract higher mathematics by balancing deep mathematical rigor with a witty, accessible writing style that even incorporates cartoons and philosophical quotes.

BOOK PAGE]]> https://mklab.gr/showthread.php?tid=255 Wed, 10 Jun 2026 03:57:19 +0300 mklabgr]]> https://mklab.gr/showthread.php?tid=255 Mathematics for Computer Science
by Eric Lehman

Summary  This text offers an introduction to Discrete Mathematics oriented toward Computer Science and Engineering. Topics covered: Fundamental concepts of Mathematics: definitions, proofs, sets, functions, elementary number theory; Discrete structures: graphs, counting; Discrete probability theory.

BOOK PAGE]]> Mathematics for Computer Science
by Eric Lehman

Summary  This text offers an introduction to Discrete Mathematics oriented toward Computer Science and Engineering. Topics covered: Fundamental concepts of Mathematics: definitions, proofs, sets, functions, elementary number theory; Discrete structures: graphs, counting; Discrete probability theory.

BOOK PAGE]]> https://mklab.gr/showthread.php?tid=238 Wed, 10 Jun 2026 03:00:05 +0300 mklabgr]]> https://mklab.gr/showthread.php?tid=238 Σημειώσεις στη Συνολοθεωρία
Γιάννη Ν. Μοσχοβάκη

Summary  Οι «Σημειώσεις στη Συνολοθεωρία» του Γιάννη Ν. Μοσχοβάκη αποτελούν βασικό σύγγραμμα για την εισαγωγή στα θεμέλια των μαθηματικών, εισάγοντας τη θεωρία συνόλων τόσο ως αυτόνομο μαθηματικό πεδίο όσο και ως τη «γλώσσα» πάνω στην οποία μοντελοποιούνται όλα τα κλασικά μαθηματικά αντικείμενα

BOOK PAGE]]> Σημειώσεις στη Συνολοθεωρία
Γιάννη Ν. Μοσχοβάκη

Summary  Οι «Σημειώσεις στη Συνολοθεωρία» του Γιάννη Ν. Μοσχοβάκη αποτελούν βασικό σύγγραμμα για την εισαγωγή στα θεμέλια των μαθηματικών, εισάγοντας τη θεωρία συνόλων τόσο ως αυτόνομο μαθηματικό πεδίο όσο και ως τη «γλώσσα» πάνω στην οποία μοντελοποιούνται όλα τα κλασικά μαθηματικά αντικείμενα

BOOK PAGE]]> https://mklab.gr/showthread.php?tid=237 Wed, 10 Jun 2026 02:56:56 +0300 mklabgr]]> https://mklab.gr/showthread.php?tid=237 Descriptive Set Theory
by Yiannis N. Moschovakis

Summary  Descriptive Set Theory is the study of sets in separable, complete metric spaces that can be defined, and so can be expected to have special properties not enjoyed by arbitrary pointsets. This monograph develops Descriptive Set Theory systematically, from its classical roots to the modern "effective" theory and the consequences of strong hypotheses. The book emphasizes the foundations of the subject, and it sets the stage for the dramatic results relating large cardinals and determinacy or allowing applications of Descriptive Set Theory to classical mathematics.

BOOK PAGE]]> Descriptive Set Theory
by Yiannis N. Moschovakis

Summary  Descriptive Set Theory is the study of sets in separable, complete metric spaces that can be defined, and so can be expected to have special properties not enjoyed by arbitrary pointsets. This monograph develops Descriptive Set Theory systematically, from its classical roots to the modern "effective" theory and the consequences of strong hypotheses. The book emphasizes the foundations of the subject, and it sets the stage for the dramatic results relating large cardinals and determinacy or allowing applications of Descriptive Set Theory to classical mathematics.

BOOK PAGE]]> https://mklab.gr/showthread.php?tid=230 Wed, 10 Jun 2026 02:37:29 +0300 mklabgr]]> https://mklab.gr/showthread.php?tid=230 An Introduction to Mathematical Reasoning
by Peter J. Eccles

Summary  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. This is achieved by exploring set theory, combinatorics and number theory, topics which include many fundamental ideas which are part of the tool kit of any mathematician.

BOOK PAGE]]> An Introduction to Mathematical Reasoning
by Peter J. Eccles

Summary  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. This is achieved by exploring set theory, combinatorics and number theory, topics which include many fundamental ideas which are part of the tool kit of any mathematician.

BOOK PAGE]]> https://mklab.gr/showthread.php?tid=224 Wed, 10 Jun 2026 02:17:06 +0300 mklabgr]]> https://mklab.gr/showthread.php?tid=224 A Friendly Introduction to Mathematical Logic
by Christopher C. Leary

Summary  At the intersection of mathematics, computer science, and philosophy, mathematical logic examines the power and limitations of formal mathematical thinking. In this edition, readers with no previous study in the field are introduced to the basics of model theory, proof theory, and computability theory. The text is designed to be used either in an upper division undergraduate classroom, or for self study.

BOOK PAGE

BOOK PAGE 2]]> A Friendly Introduction to Mathematical Logic
by Christopher C. Leary

Summary  At the intersection of mathematics, computer science, and philosophy, mathematical logic examines the power and limitations of formal mathematical thinking. In this edition, readers with no previous study in the field are introduced to the basics of model theory, proof theory, and computability theory. The text is designed to be used either in an upper division undergraduate classroom, or for self study.

BOOK PAGE

BOOK PAGE 2]]> https://mklab.gr/showthread.php?tid=211 Wed, 10 Jun 2026 01:22:24 +0300 mklabgr]]> https://mklab.gr/showthread.php?tid=211 A Gentle Introduction to the Art of Mathematics
by Joseph Fields

Summary  The point of this book is to help you with the transition from doing math at an elementary level (which is concerned mostly with solving problems) to doing math at an advanced level (which is much more concerned with axiomatic systems and proving statements within those systems).

BOOK PAGE]]> A Gentle Introduction to the Art of Mathematics
by Joseph Fields

Summary  The point of this book is to help you with the transition from doing math at an elementary level (which is concerned mostly with solving problems) to doing math at an advanced level (which is much more concerned with axiomatic systems and proving statements within those systems).

BOOK PAGE]]> https://mklab.gr/showthread.php?tid=195 Wed, 10 Jun 2026 00:02:16 +0300 mklabgr]]> https://mklab.gr/showthread.php?tid=195 Handbook of Mathematical Proof
by Edward D. Kim

Summary  This can be used for an intro to proofs course, or a reference in a proof-based course. Designing any guide or text on mathematical proof leads to a discussion of sets first or propositions first. We introduce a little of each first, and then constantly bring the discussion back to categorizing what each kind of thing is, with emphasis on mathematical language.

BOOK PAGE]]> Handbook of Mathematical Proof
by Edward D. Kim

Summary  This can be used for an intro to proofs course, or a reference in a proof-based course. Designing any guide or text on mathematical proof leads to a discussion of sets first or propositions first. We introduce a little of each first, and then constantly bring the discussion back to categorizing what each kind of thing is, with emphasis on mathematical language.

BOOK PAGE]]>