https://doi.org/10.1142/11973 | December 2020
Pages: 244
College students struggle with the switch from thinking of mathematics as a calculation based subject to a problem solving based subject. This book describes how the introduction to proofs course can be taught in a way that gently introduces students to this new way of thinking. This introduction utilizes recent research in neuroscience regarding how the brain learns best. Rather than jumping right into proofs, students are first taught how to change their mindset about learning, how to persevere through difficult problems, how to work successfully in a group, and how to reflect on their learning. With these tools in place, students then learn logic and problem solving as a further foundation.
Next various proof techniques such as direct proofs, proof by contraposition, proof by contradiction, and mathematical induction are introduced. These proof techniques are introduced using the context of number theory. The last chapter uses Calculus as a way for students to apply the proof techniques they have learned.
Pedagogical Notes for Professors
Brain Growth
Team Building
Setting Goals
Logic
Problem Solving
Study Techniques
Pre-proofs
Direct Proofs (Even, Odd, & Divides)
Direct Proofs (Rational, Prime, & Composite)
Direct Proofs (Square Numbers & Absolute Value)
Direct Proofs (GCD & Relatively Prime)
Proof by Division into Cases
Proof by Division into Cases (Quotient Remainder Theorem)
Forward-Backward Proofs
Proof by Contraposition
Proof by Contradiction
Mathematical Induction
Mathematical Induction Part II
Appendices:
Broken Circles Activity
Answers for Hiking Activity
Escape Room
Proof for Exercise 17.12
Selected Proofs from All Chapters
Proof Methods
Proof Template
References
Homework Log
Undergraduate in mathematics majors, for use in an undergraduate introduction to mathematical proofs course.
https://doi.org/10.1142/11802 | December 2020
Pages: 252
ISBN: 978-981-122-007-4 (hardcover)
ISBN: 978-981-121-943-6 (softcover)
Origami, paper folding, originated hundreds of years ago in China and Japan, with independent discovery and activity across the world. The most familiar origami models are the crane and the flapping bird. This book will introduce you to origami, starting with a jumping frog and including traditional and modern models. Carefully written instructions, using photos and diagrams, will show you the main origami bases, turn you into a successful folder and stimulate your own creativity. Explanations will include attention to spatial relations, geometry, algebra, and pattern finding. The explanations provide insight into the origami while the folding will help your understanding of mathematics.
Magazine Cover Box and Business Card Frog:
Dividing a Rectangle into Quarters: Geometry
Computation of Hem Size: Algebra
Fluttering Butterfly and Star Basket:
Introduction to Geometry and Trigonometry
Computation of Final Dimension
Waterbomb, Tulip, and Stellated Octahedron :
Comparison of Models: Exercise in Seeing Categories
2D to 3D to 2D: Surface Area Exercise for Waterbomb
Fractions (Generating Folds at 1/8, 1/4, 3/8, 1/2, 5/8, 3/4 Positions Along a Line)
Drinking Cup:
Making Square from a Rectangle: Geometry
Contrasting Making a Fold with the Goal of Making a New Edge Parallel to an Existing Edge with the More Typical Folds of Edge to Edge or Point to Point
Proving the Uniqueness of Three Points Made by the Fold by Calculating Distances Using Geometry and Trigonometry
Waterbomb Base Ornament and King David Crown:
First Experiences with Modular (Unit) Construction
Calculation of Final Dimension Using Geometry
Contrast Two Models in Use of 2D (Flat) versus 3D Units
Flapping Bird and Crane:
Understand Action of Flapping Bird and Contrast with Crane
Compare Different Folding Methods and Crease Patterns Using Spatial Relations
Calculate Wingspan of Flapping Bird Using Geometry
Traditional Frog on Lily Pad:
2D to 3D for Frog: Spatial Relations
Examine Relationship of Crease Patterns of Bases: Pattern Finding Based on Observations of Peter Engel
Final Dimensions Using Geometry
For all ages, especially students in college classrooms. Good for home schooling and supplement for K-12 remote learning.
https://doi.org/10.1142/11803 | December 2020
Pages: 276
ISBN: 978-981-122-008-1 (hardcover)
ISBN: 978-981-121-946-7 (softcover)
Origami, paper folding, originated hundreds of years ago in China and Japan, with independent discovery across the world. Today people do origami, create new models, share their work, and discover mathematical principles. This book continues the approach of Origami with Explanations; but is independent, with basic instructions repeated. Carefully written instructions, using photos and diagrams, will turn you into a successful folder and stimulate your own creativity. The models in this book include action models, money folds, beautiful and useful containers, and modular origami. Mathematics topics touched on include improving estimates, tessellations, mathematical induction, flat-foldability, and fold-and-cut. The Explanations section provide insight into the origami and introduce or re-introduce you to basic and advanced subjects in mathematics.
Kissy Fish:
3 Ways to Determine Thirds:
Informal S Method Using Property of Thirds
Improving Estimate Using Standard Reduction of Error Term (Iteration, Powers of 2)
Analytic Geometry: Define Coordinate System and Solve Equations
Reprise on Sinks, Reverse Folds and Squash Folds, Pointing Out the Common Feature of Changing the Sense of Some Folds (Spatial Relations)
Tetrahedrons:
Prove Strip Method Produces Equilateral Triangles Using Geometry
Introduction to Platonic Solids: Classic 3D Geometry
Introduction to Tessellations with Proof That Only Certain Regular Polygons Tessellate (Tile the Plane)
Heart Locket:
Construction of Marks at 3/8 and 5/8 (or 1/8 and 7/8) Positions: Fractions
Examination of Construction, 2D to 3D: Spatial Relations
One-Dollar Shirt and Dollar Bill Heart:
One-Dollar Shirt Construction: Spatial Relations
Broken Heart: Bisecting Angles: Geometry
Broken Heart: Examining the Mechanism: Spatial Relations
Broken Heart: Calculating Certain Dimensions: Algebra, Trigonometry
Compare Size of the 2 Heart Configurations: Geometry
Dollar Bill Rosette:
Iteration to Improve Estimate: Similar to A Method for Thirds, Property of 11
Identified Category of Primes by Writing A Program: Full Reptend Primes Base 2
Prove Equivalence of Folding Property to A Category of Primes: Algebraic Manipulation and Mathematical Induction
Exercise: Compare to Jackson 16 Panel Version
Masu Box and Shen Basket:
Rigidity from Layers
Final Dimensions Using Crease Pattern and Geometry
Directions to Making Lid, Pointing Out How It Does Not Scale to Size of Paper
Brief Description of Origami Mathematics Flat Foldability Conditions and How One Condition is Violated at One Point in Folding Shen Basket
Peek into Crease Pattern Origami (Reference to Robert Lang's Treemaker)
Ninja Star and Stackable Cubes:
Number of Layers in Ninja Star and in Cube
Handedness: Geometry, Transformations and Spatial Relations
Comparisons to Other Modular Models
Stack of Cubes as 2nd Order Modular
One-Snip 5-Pointed Star and One-Snip Square Letter O:
How to Produce Square Letter 0: Spatial Relations, Patterns
Brief Mention of Theorem (2 Approaches) on Generality of One-Snip for Polygons, an Acclaimed Example of Origami Mathematics
For all ages, especially students in college classrooms. Good for home schooling and supplement for K-12 remote learning.
World Scientific Series on Science Communication: Volume 2
https://doi.org/10.1142/11970 | December 2020
Pages: 168
ISBN: 978-981-122-544-4 (hardcover)
A highly rigorous, yet original and entertaining book that explores the connection between food and science.
Why has science forcefully entered the kitchen from a certain moment in history?
Why do scientists often use images and metaphors drawn from gastronomy?
What is the common thread that connects scientific experiments to mouth-watering recipes?
What has futurist cooking got in common with molecular gastronomy?
Experients with coffee, controversies over beer and chocolate recipes guarded as if they were secret patents are the ingredients of this original, surprising account of the intersections between gastronomy and research, between laboratories and kitchens.
Cookery as Science, and Science as Cookery: From Socrates to Cold Fusion
The Science of Chicken
Beer, Wine, Coffee, Tea, Chocolate and ... as Many Controversies as You Like
A Taste of Science (and Society): From Brillat-Savarin to Molecular Cooking via Futuristic Cooking
General.
https://doi.org/10.1142/12059 | February 2021
Pages: 265
ISBN: 978-981-122-883-4 (hardcover)
ISBN: 978-981-122-953-4 (softcover)
You have access to thisebook
The third edition of this book aims to equip both young and experienced researchers with all the tools and strategy they will need for their papers to not just be accepted, but stand out in the crowded field of academic publishing. It seeks to question and deconstruct the legacy of existing science writing, replacing or supporting historically existing practices with principle- and evidence-driven styles of effective writing. It encourages a reader-centric approach to writing, satisfying reader-scientists at large, but also the paper's most powerful readers, the reviewer and editor. Going beyond the baseline of well-structured scientific writing, this book leverages an understanding of human physiological limitations (memory, attention, time) to help the author craft a document that is optimized for readability.
Through real and fictional examples, hands-on exercises, and entertaining stories, this book breaks down the critical parts of a typical scientific paper (Title, Abstract, Introduction, Visuals, Structure, and Conclusions). It shows at great depth how to achieve the essential qualities required in scientific writing, namely being clear, concise, convincing, fluid, interesting, and organized. To enable the writer to assess whether these parts are well written from a reader's perspective, the book also offers practical metrics in the form of six checklists, and even an original Java application to assist in the evaluation.
Doctoral students, PhDs, postdocs, associate professors, principal investigators, junior faculty, research scientists, clinicians.
Selected Writings on Recreational Mathematics and its History
(Volume 1)
https://doi.org/10.1142/11977-vol1 | March 2021
Pages: 300
ISBN: 978-981-122-600-7 (hardcover)
ISBN: 978-981-122-650-2 (softcover)
This volume is part of a reference set. To view or order the whole set, please visit the main page
The author believes in the presentation and teaching of mathematics as recreation. When the Rubik's Cube took off in 1978, based on thinly disguised mathematics, he became seriously interested in mathematical puzzles which would provide mental stimulation for students and professional mathematicians.
In these 2-volume books, the readers shall have an adventure into previously unknown origins of ancient puzzles, which could be traced back to their Medieval, Chinese, Arabic and Indian sources. The puzzles are fully described, many with illustrations, adding interest to their history and relevance to contemporary mathematical concepts.
What is Recreational Mathematics?
The Utility of Recreational Mathematics
Ancient Puzzles
Puzzles from The Greek Anthology
Aryabhata and Other Early Indian Mathematicians
Alcuin and his Propositiones
The Problems of Abbot Albert
Luca Pacioli's De Viribus Quantitatis
Luca Pacioli's Magic and Card Tricks
Some Early Topological Puzzles
Finding a Sardinian Maze
Students and scholars of mathematics and its history, Maths teachers, general public.