https://mklab.gr/ Wed, 29 Jul 2026 01:26:56 +0000 MyBB https://mklab.gr/showthread.php?tid=98 Fri, 05 Jun 2026 16:09:01 +0300 mklabgr]]> https://mklab.gr/showthread.php?tid=98 Title The Essence of Mathematics Through Elementary Problems
Author Alexandre Borovik  and Tony Gardiner

Summary  

It is increasingly clear that the shapes of reality – whether of the natural world, or of the built environment – are in some profound sense mathematical. Therefore it would benefit students and educated adults to understand what makes mathematics itself ‘tick’, and to appreciate why its shapes, patterns and formulae provide us with precisely the language we need to make sense of the world around us. The second part of this challenge may require some specialist experience, but the authors of this book concentrate on the first part, and explore the extent to which elementary mathematics allows us all to understand something of the nature of mathematics from the inside.

The Essence of Mathematics consists of a sequence of 270 problems – with commentary and full solutions. The reader is assumed to have a reasonable grasp of school mathematics. More importantly, s/he should want to understand something of mathematics beyond the classroom, and be willing to engage with (and to reflect upon) challenging problems that highlight the essence of the discipline.

The book consists of six chapters of increasing sophistication (Mental Skills; Arithmetic; Word Problems; Algebra; Geometry; Infinity), with interleaved commentary. The content will appeal to students considering further study of mathematics at university, teachers of mathematics at age 14-18, and anyone who wants to see what this kind of elementary content has to tell us about how mathematics really works.

BOOK PAGE

]]> Title The Essence of Mathematics Through Elementary Problems
Author Alexandre Borovik  and Tony Gardiner

Summary  

It is increasingly clear that the shapes of reality – whether of the natural world, or of the built environment – are in some profound sense mathematical. Therefore it would benefit students and educated adults to understand what makes mathematics itself ‘tick’, and to appreciate why its shapes, patterns and formulae provide us with precisely the language we need to make sense of the world around us. The second part of this challenge may require some specialist experience, but the authors of this book concentrate on the first part, and explore the extent to which elementary mathematics allows us all to understand something of the nature of mathematics from the inside.

The Essence of Mathematics consists of a sequence of 270 problems – with commentary and full solutions. The reader is assumed to have a reasonable grasp of school mathematics. More importantly, s/he should want to understand something of mathematics beyond the classroom, and be willing to engage with (and to reflect upon) challenging problems that highlight the essence of the discipline.

The book consists of six chapters of increasing sophistication (Mental Skills; Arithmetic; Word Problems; Algebra; Geometry; Infinity), with interleaved commentary. The content will appeal to students considering further study of mathematics at university, teachers of mathematics at age 14-18, and anyone who wants to see what this kind of elementary content has to tell us about how mathematics really works.

BOOK PAGE

]]> https://mklab.gr/showthread.php?tid=88 Fri, 05 Jun 2026 15:38:53 +0300 mklabgr]]> https://mklab.gr/showthread.php?tid=88 Title : Street Fighting Mathematics 
Author : Sanjoy Mahajan

Summary : Street-Fighting Mathematics: The Art of Educated Guessing and Opportunistic Problem Solving by Sanjoy Mahajan is a brilliant, practical guide that teaches scientists and engineers how to estimate answers and solve complex problems without requiring rigid, formal proofs

BOOK PAGE]]> Title : Street Fighting Mathematics 
Author : Sanjoy Mahajan

Summary : Street-Fighting Mathematics: The Art of Educated Guessing and Opportunistic Problem Solving by Sanjoy Mahajan is a brilliant, practical guide that teaches scientists and engineers how to estimate answers and solve complex problems without requiring rigid, formal proofs

BOOK PAGE]]> https://mklab.gr/showthread.php?tid=78 Wed, 03 Jun 2026 22:14:07 +0300 mklabgr]]> https://mklab.gr/showthread.php?tid=78 Advanced Problems in Mathematics , Preparing for University
Author : Stephen Siklos

Summary :  This book is intended to help candidates prepare for entrance examinations in mathematics and scientific subjects, including STEP (Sixth Term Examination Paper). STEP is an examination used by Cambridge colleges as the basis for conditional offers. 

SOURCE]]> Advanced Problems in Mathematics , Preparing for University
Author : Stephen Siklos

Summary :  This book is intended to help candidates prepare for entrance examinations in mathematics and scientific subjects, including STEP (Sixth Term Examination Paper). STEP is an examination used by Cambridge colleges as the basis for conditional offers. 

SOURCE]]> https://mklab.gr/showthread.php?tid=71 Mon, 01 Jun 2026 22:13:56 +0300 mklabgr]]> https://mklab.gr/showthread.php?tid=71 A Collection of Problems, with Solutions and Comments by Andrew Adler

SOURCE]]> A Collection of Problems, with Solutions and Comments by Andrew Adler

SOURCE]]> https://mklab.gr/showthread.php?tid=69 Mon, 01 Jun 2026 21:56:44 +0300 mklabgr]]> https://mklab.gr/showthread.php?tid=69 Title :  Methods Of Solving Problems In High School Mathematics

Authors :  A. G. Tsypkin; A. I. Pinsky ; V. I. Blagodatskikh (Editor)

"Methods of Solving Problems in High-School Mathematics" (A. G. Tsypkin & A. I. Pinsky, Mir Publishers, 1986) is a classic Soviet study guide designed to prepare students for rigorous university entrance exams.
Instead of just grouping math by topic, the book is organized around the specific logical methods used to solve problems.

• The Scope: It bridges standard algebra, geometry, and trigonometry with advanced topics like vector algebra, limits, and introductory calculus.
  
• The Methodology: It teaches readers how to combine disciplines—such as using algebraic transformations alongside calculus to solve a single complex problem.
  
• The Volume: It contains roughly 2,500 problems. Many are left intentionally without fully worked-out solutions to force active, independent practice.
  

SOURCE]]> Title :  Methods Of Solving Problems In High School Mathematics

Authors :  A. G. Tsypkin; A. I. Pinsky ; V. I. Blagodatskikh (Editor)

"Methods of Solving Problems in High-School Mathematics" (A. G. Tsypkin & A. I. Pinsky, Mir Publishers, 1986) is a classic Soviet study guide designed to prepare students for rigorous university entrance exams.
Instead of just grouping math by topic, the book is organized around the specific logical methods used to solve problems.

• The Scope: It bridges standard algebra, geometry, and trigonometry with advanced topics like vector algebra, limits, and introductory calculus.
  
• The Methodology: It teaches readers how to combine disciplines—such as using algebraic transformations alongside calculus to solve a single complex problem.
  
• The Volume: It contains roughly 2,500 problems. Many are left intentionally without fully worked-out solutions to force active, independent practice.
  

SOURCE]]> https://mklab.gr/showthread.php?tid=68 Mon, 01 Jun 2026 21:51:34 +0300 mklabgr]]> https://mklab.gr/showthread.php?tid=68 These notes are an introduction to the art of mathematical problem solving. This means solving the type of problems that usually are posed in competitions (like the Putnam Competition or the International Mathematical Olympiad) or in journals (like the American Mathematical Monthly or Crux Mathematicorum1 ):

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SOURCE]]> These notes are an introduction to the art of mathematical problem solving. This means solving the type of problems that usually are posed in competitions (like the Putnam Competition or the International Mathematical Olympiad) or in journals (like the American Mathematical Monthly or Crux Mathematicorum1 ):

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SOURCE]]>