https://mklab.gr/ Sat, 13 Jun 2026 09:17:56 +0000 MyBB https://mklab.gr/showthread.php?tid=306 Fri, 12 Jun 2026 23:35:33 +0300 mklabgr]]> https://mklab.gr/showthread.php?tid=306



A Guide to Infinity Ten Mathematical Journeys
Edward R. Scheinerman

Summary 

A Guide to Infinity: Ten Mathematical Journeys by Edward R. Scheinerman (Yale University Press) is an accessible yet rigorous exploration of how mathematicians conceptualize, structure, and utilize the infinite.
Rather than treating infinity as a philosophical paradox, Scheinerman presents it as a practical, highly organized tool through ten distinct "journeys":

• Arithmetic & Number Systems: It explores adding $\pm\infty$ to the real number line, "tropical arithmetic" (which redefines addition and multiplication using minimums), and hyperreal numbers (which formally incorporate infinite and infinitesimal values).
  
• Geometry: It dives into the projective plane (where parallel lines meet at an infinite horizon) and non-Euclidean geometry via the hyperbolic plane.
  
• Set Theory & Logic: It covers transfinite cardinal and ordinal numbers, explaining the different sizes of infinity and looking at the implications of the Continuum Hypothesis.
  
• Visual Infinity: It concludes with the infinite self-similarity found in fractals.
  

Tone & Approach: Written with witty, engaging prose, the book balances conceptual explanations with precise mathematical definitions and theorems. Functioning like an advanced lecture series, each chapter ends with open-ended questions designed to prompt active exploration, making it a great fit for undergraduate students, science enthusiasts, and the mathematically curious.

BOOK PAGE]]>



A Guide to Infinity Ten Mathematical Journeys
Edward R. Scheinerman

Summary 

A Guide to Infinity: Ten Mathematical Journeys by Edward R. Scheinerman (Yale University Press) is an accessible yet rigorous exploration of how mathematicians conceptualize, structure, and utilize the infinite.
Rather than treating infinity as a philosophical paradox, Scheinerman presents it as a practical, highly organized tool through ten distinct "journeys":

• Arithmetic & Number Systems: It explores adding $\pm\infty$ to the real number line, "tropical arithmetic" (which redefines addition and multiplication using minimums), and hyperreal numbers (which formally incorporate infinite and infinitesimal values).
  
• Geometry: It dives into the projective plane (where parallel lines meet at an infinite horizon) and non-Euclidean geometry via the hyperbolic plane.
  
• Set Theory & Logic: It covers transfinite cardinal and ordinal numbers, explaining the different sizes of infinity and looking at the implications of the Continuum Hypothesis.
  
• Visual Infinity: It concludes with the infinite self-similarity found in fractals.
  

Tone & Approach: Written with witty, engaging prose, the book balances conceptual explanations with precise mathematical definitions and theorems. Functioning like an advanced lecture series, each chapter ends with open-ended questions designed to prompt active exploration, making it a great fit for undergraduate students, science enthusiasts, and the mathematically curious.

BOOK PAGE]]> https://mklab.gr/showthread.php?tid=305 Fri, 12 Jun 2026 23:29:13 +0300 mklabgr]]> https://mklab.gr/showthread.php?tid=305 Visions of Infinity: The Great Mathematical Problems
by Ian Stewart

Summary 

[b]Visions of Infinity: The Great Mathematical Problems (2013) by acclaimed science writer Ian Stewart explores 14 of the most famous, elusive, and consequential puzzles in mathematical history.[/b]

• [b]The Core Premise: Stewart argues that the true value of a "Great Problem" isn't just finding the answer; it is the entirely new fields of science, technology, and logical techniques that are invented along the way while trying to solve it.[/b]
  
• [b]The Puzzles: The book covers a mix of historic milestones, famously solved riddles, and ongoing multi-million-dollar Millennium Prize problems. These include Fermat’s Last Theorem (solved by Andrew Wiles), the Poincaré Conjecture (solved by Grigori Perelman), the Riemann Hypothesis (the "Holy Grail" of prime numbers), and computer science's ultimate question, P vs. NP.[/b]
  
• [b]The Narrative: Rather than bogging the reader down in dense formulas, Stewart uses accessible analogies and historical anecdotes. He highlights the human element—the eccentric, brilliant, and sometimes obsessive geniuses who dedicated their lives to these challenges.[/b]
  

In short: It is an engaging, highly accessible history of mathematics told through its greatest mysteries, showing how abstract, impractical questions ultimately build the foundation for our modern technological world.

BOOK PAGE]]> Visions of Infinity: The Great Mathematical Problems
by Ian Stewart

Summary 

[b]Visions of Infinity: The Great Mathematical Problems (2013) by acclaimed science writer Ian Stewart explores 14 of the most famous, elusive, and consequential puzzles in mathematical history.[/b]

• [b]The Core Premise: Stewart argues that the true value of a "Great Problem" isn't just finding the answer; it is the entirely new fields of science, technology, and logical techniques that are invented along the way while trying to solve it.[/b]
  
• [b]The Puzzles: The book covers a mix of historic milestones, famously solved riddles, and ongoing multi-million-dollar Millennium Prize problems. These include Fermat’s Last Theorem (solved by Andrew Wiles), the Poincaré Conjecture (solved by Grigori Perelman), the Riemann Hypothesis (the "Holy Grail" of prime numbers), and computer science's ultimate question, P vs. NP.[/b]
  
• [b]The Narrative: Rather than bogging the reader down in dense formulas, Stewart uses accessible analogies and historical anecdotes. He highlights the human element—the eccentric, brilliant, and sometimes obsessive geniuses who dedicated their lives to these challenges.[/b]
  

In short: It is an engaging, highly accessible history of mathematics told through its greatest mysteries, showing how abstract, impractical questions ultimately build the foundation for our modern technological world.

BOOK PAGE]]> https://mklab.gr/showthread.php?tid=304 Fri, 12 Jun 2026 23:21:48 +0300 mklabgr]]> https://mklab.gr/showthread.php?tid=304

Mathematical Explorations for Young Minds
Adventures on the Island of Oxisz
Authors Bálint Hujter , Dániel Lenger , Gábor Szűcs

Summary Mathematical Explorations for Young Minds: Adventures on the Island of Oxisz (Springer, 2024) by Bálint Hujter, Dániel Lenger, and Gábor Szűcs is an engaging problem-solving book designed for students aged 12 and up, educators, and competition trainers.

• The Concept: It frames abstract math problems as a fictional adventure. Readers follow three friends—Albrecht, Tarkal, and Zsordi—across 14 journeys to the mysterious Island of Oxisz.
  
• The Puzzles: It features 84 interconnected problems adapted from Hungary's renowned Dürer Competition. The problems focus on creative thinking, logic, combinatorics, and geometry rather than rote formulas.
  
• Difficulty: While it requires only basic middle-school math knowledge, the problems are genuinely challenging and require out-of-the-box lateral thinking.
  
• Support: The book includes a structured "Hints" section to guide readers when they get stuck, followed by full, step-by-step solutions.
  

In short: It is a playful yet rigorous textbook that uses a fantasy adventure narrative to teach high-level mathematical problem-solving.

BOOK PAGE]]>

Mathematical Explorations for Young Minds
Adventures on the Island of Oxisz
Authors Bálint Hujter , Dániel Lenger , Gábor Szűcs

Summary Mathematical Explorations for Young Minds: Adventures on the Island of Oxisz (Springer, 2024) by Bálint Hujter, Dániel Lenger, and Gábor Szűcs is an engaging problem-solving book designed for students aged 12 and up, educators, and competition trainers.

• The Concept: It frames abstract math problems as a fictional adventure. Readers follow three friends—Albrecht, Tarkal, and Zsordi—across 14 journeys to the mysterious Island of Oxisz.
  
• The Puzzles: It features 84 interconnected problems adapted from Hungary's renowned Dürer Competition. The problems focus on creative thinking, logic, combinatorics, and geometry rather than rote formulas.
  
• Difficulty: While it requires only basic middle-school math knowledge, the problems are genuinely challenging and require out-of-the-box lateral thinking.
  
• Support: The book includes a structured "Hints" section to guide readers when they get stuck, followed by full, step-by-step solutions.
  

In short: It is a playful yet rigorous textbook that uses a fantasy adventure narrative to teach high-level mathematical problem-solving.

BOOK PAGE]]> https://mklab.gr/showthread.php?tid=287 Thu, 11 Jun 2026 18:45:31 +0300 mklabgr]]> https://mklab.gr/showthread.php?tid=287



Problem-Solving and Selected Topics in Euclidean Geometry
Authors Sotirios E. Louridas , Michael Th. Rassias

Sumary
 [b]"Problem-Solving and Selected Topics in Euclidean Geometry: In the Spirit of the Mathematical Olympiads" by S. E. Louridas and M. Th. Rassias:[/b]

• [b]Purpose: A specialized guide tailored for students and teachers preparing for high-level Mathematical Olympiads.[/b]
  
• [b]Content: It covers fundamental theorems, geometric loci, and transformations, offering a collection of challenging Olympiad-level problems with fully detailed solutions.[/b]
  
• [b]Approach: Instead of just giving answers, it provides a "key idea" before each solution to help readers develop structured mathematical intuition and problem-solving strategies.[/b]
  
• [b]Target Audience: Ideal for advanced high school students, math circle instructors, and anyone passionate about competitive geometry.[/b]
  

BOOK PAGE]]>



Problem-Solving and Selected Topics in Euclidean Geometry
Authors Sotirios E. Louridas , Michael Th. Rassias

Sumary
 [b]"Problem-Solving and Selected Topics in Euclidean Geometry: In the Spirit of the Mathematical Olympiads" by S. E. Louridas and M. Th. Rassias:[/b]

• [b]Purpose: A specialized guide tailored for students and teachers preparing for high-level Mathematical Olympiads.[/b]
  
• [b]Content: It covers fundamental theorems, geometric loci, and transformations, offering a collection of challenging Olympiad-level problems with fully detailed solutions.[/b]
  
• [b]Approach: Instead of just giving answers, it provides a "key idea" before each solution to help readers develop structured mathematical intuition and problem-solving strategies.[/b]
  
• [b]Target Audience: Ideal for advanced high school students, math circle instructors, and anyone passionate about competitive geometry.[/b]
  

BOOK PAGE]]> https://mklab.gr/showthread.php?tid=286 Thu, 11 Jun 2026 18:37:52 +0300 mklabgr]]> https://mklab.gr/showthread.php?tid=286




Διαγωνισμοί στα Μαθηματικά Β΄ και Γ΄ Λυκείου
Συγγραφεις ¨ Μάγκος Αθανάσιος, Χριστοφίδης Δημήτρης, Στεργίου Χαράλαμπος, Συγκελάκης Αλέξανδρος, Μουρούκος Ευάγγελος

Περίκηψη

Το βιβλίο «Διαγωνισμοί στα Μαθηματικά Β΄ και Γ΄ Λυκείου – 1ος τόμος (Γεωμετρία | Συνδυαστική)» (Εκδόσεις Σαββάλας, 2020) συντάχθηκε από μια ομάδα έμπειρων μαθηματικών (Α. Μάγκος, Δ. Χριστοφίδης, Χ. Στεργίου, Α. Συγκελάκης, Ε. Μουρούκος) και αποτελεί έναν πλήρη οδηγό προετοιμασίας για τους μαθηματικούς διαγωνισμούς της ΕΜΕ («Θαλής», «Ευκλείδης», «Αρχιμήδης»), καθώς και για τους προκριματικούς των Εθνικών Ομάδων.

ΤΟΜΟΣ 1

ΤΟΜΟΣ 2]]>




Διαγωνισμοί στα Μαθηματικά Β΄ και Γ΄ Λυκείου
Συγγραφεις ¨ Μάγκος Αθανάσιος, Χριστοφίδης Δημήτρης, Στεργίου Χαράλαμπος, Συγκελάκης Αλέξανδρος, Μουρούκος Ευάγγελος

Περίκηψη

Το βιβλίο «Διαγωνισμοί στα Μαθηματικά Β΄ και Γ΄ Λυκείου – 1ος τόμος (Γεωμετρία | Συνδυαστική)» (Εκδόσεις Σαββάλας, 2020) συντάχθηκε από μια ομάδα έμπειρων μαθηματικών (Α. Μάγκος, Δ. Χριστοφίδης, Χ. Στεργίου, Α. Συγκελάκης, Ε. Μουρούκος) και αποτελεί έναν πλήρη οδηγό προετοιμασίας για τους μαθηματικούς διαγωνισμούς της ΕΜΕ («Θαλής», «Ευκλείδης», «Αρχιμήδης»), καθώς και για τους προκριματικούς των Εθνικών Ομάδων.

ΤΟΜΟΣ 1

ΤΟΜΟΣ 2]]> https://mklab.gr/showthread.php?tid=102 Fri, 05 Jun 2026 18:36:14 +0300 mklabgr]]> https://mklab.gr/showthread.php?tid=102

Learning Geometry Through Problem Solving

Author : Boris Pritsker

Summary : This new volume offers a comprehensive collection of secondary school-level plane geometry problems, evenly balanced between proofs, calculations, and ruler-and-compass constructions.
Book Structure

• Introduction: Covers core problem-solving strategies and warm-up exercises.
  
• Core Chapters: Four dedicated chapters ("Triangles," "Quadrilaterals," "Circles," and "Areas") are split into three sections that progress from basic concepts to advanced Olympiad-level challenges.
  
• Conclusion: A final chapter of mixed, complex problems.
  

Key Features

• Full Solutions: Includes detailed answers for every problem, often featuring multiple alternative methods to build insight and strategy.
  
• Goal: Designed to build mathematical confidence, reveal connections between geometric concepts, and make learning geometry an enjoyable experience.
  

BOOK PAGE]]>

Learning Geometry Through Problem Solving

Author : Boris Pritsker

Summary : This new volume offers a comprehensive collection of secondary school-level plane geometry problems, evenly balanced between proofs, calculations, and ruler-and-compass constructions.
Book Structure

• Introduction: Covers core problem-solving strategies and warm-up exercises.
  
• Core Chapters: Four dedicated chapters ("Triangles," "Quadrilaterals," "Circles," and "Areas") are split into three sections that progress from basic concepts to advanced Olympiad-level challenges.
  
• Conclusion: A final chapter of mixed, complex problems.
  

Key Features

• Full Solutions: Includes detailed answers for every problem, often featuring multiple alternative methods to build insight and strategy.
  
• Goal: Designed to build mathematical confidence, reveal connections between geometric concepts, and make learning geometry an enjoyable experience.
  

BOOK PAGE]]> https://mklab.gr/showthread.php?tid=101 Fri, 05 Jun 2026 17:26:04 +0300 mklabgr]]> https://mklab.gr/showthread.php?tid=101


Title : Introduction to Experimental Mathematics (Cambridge Mathematical Textbooks) 1st Edition
Author : Søren Eilers, Rune Johansen
Date : 2017

Summary :  Introduction to Experimental Mathematics (by Søren Eilers and Rune Johansen, published by Cambridge University Press) is a highly practical textbook designed to bridge the gap between traditional theoretical mathematics and computational exploration.

BOOK PAGE]]>


Title : Introduction to Experimental Mathematics (Cambridge Mathematical Textbooks) 1st Edition
Author : Søren Eilers, Rune Johansen
Date : 2017

Summary :  Introduction to Experimental Mathematics (by Søren Eilers and Rune Johansen, published by Cambridge University Press) is a highly practical textbook designed to bridge the gap between traditional theoretical mathematics and computational exploration.

BOOK PAGE]]> https://mklab.gr/showthread.php?tid=100 Fri, 05 Jun 2026 17:10:48 +0300 mklabgr]]> https://mklab.gr/showthread.php?tid=100 ΣΚΟΠΟς ΑΥΤΟΥ ΤΟΥ YΠΟ-ΦΟΡΟΥΜ ΘΑ ΕΙΝΑΙ Η ΑΝΑΦΟΡΑ ΣΕ ΝΕΑ ΒΙΒΛΙΑ ΠΟΥ ΕΚΔΙΔΟΝΤΑΙ ΓΙΑ ΤΑ ΜΑΘΗΜΑΤΙΚΑ. 

"The purpose of this sub-forum will be to report on new books published about mathematics.]]> ΣΚΟΠΟς ΑΥΤΟΥ ΤΟΥ YΠΟ-ΦΟΡΟΥΜ ΘΑ ΕΙΝΑΙ Η ΑΝΑΦΟΡΑ ΣΕ ΝΕΑ ΒΙΒΛΙΑ ΠΟΥ ΕΚΔΙΔΟΝΤΑΙ ΓΙΑ ΤΑ ΜΑΘΗΜΑΤΙΚΑ. 

"The purpose of this sub-forum will be to report on new books published about mathematics.]]>