Strange Math Books That Will Make You Wonder
TLDRThis video explores 10 peculiar math books, ranging from basic to highly advanced topics. It features 'The Theory of Spinors' by Élie Cartan, a rare pamphlet by G.H. Hardy, and 'Spherical Trigonometry,' which is no longer commonly taught. The video also delves into niche areas like origami mathematics, Ramanujan's self-study book, and books of counterexamples in topology and analysis. It highlights the intriguing and sometimes bizarre nature of these mathematical works, which are both educational and a testament to the diversity within the field.
Takeaways
- 📚 The video introduces 10 unique math books, ranging from basic to advanced levels, each with a distinctive and intriguing aspect.
- 🌀 'The Theory of Spinors' by Élie Cartan is highlighted as a significant work in the field of quantum mechanics, with a focus on spinors and their general theory.
- 📖 A pamphlet titled 'Cambridge Tracks in Mathematics and Mathematical Physics' is mentioned, which is a supplement to standard textbooks on indefinite integration by G.H. Hardy.
- 📚 'Spherical Trigonometry' by Raymond W. Brink is noted for being a subject that is no longer commonly taught, yet the book provides a comprehensive look at the topic.
- 🎨 'Origami Tree: Mathematical Methods in Paper Folding' by Thomas C. Hull is praised for its authoritative approach to the mathematics of paper folding, combining classic and modern results.
- 📘 Ramanujan's self-education through 'A Synopsis of Elementary Results in Pure and Applied Mathematics' by George Escar is highlighted, showcasing the book's depth and breadth of mathematical results.
- 🔍 'Counterexamples in Topology' is described as a valuable resource for understanding exceptions to general mathematical principles in the field of topology.
- 📊 'Counterexamples in Analysis' provides a collection of unusual mathematical examples that challenge common theorems and assumptions in calculus and analysis.
- 🤓 'Calculus and Common Sense' is a comic book that presents serious calculus concepts in a fun and engaging way, suitable for those looking for a different approach to learning calculus.
- 🔮 'Methods of the Theory of Functions of Several Complex Variables' by Vladimirov is an advanced book suitable for graduate studies, covering complex and sophisticated mathematical concepts.
- 📐 'A Book of Curves' by E.H. Lockwood covers a wide array of special curves and their geometrical properties, appealing to those interested in the art and science of graphing.
Q & A
What is the subject of the book 'The Theory of Spinors' by Élie Cartan?
-The book 'The Theory of Spinors' by Élie Cartan focuses on spinors, which were first used by physicists in the field of quantum mechanics. Élie Cartan is known for his extensive work on spinors and discovering them in their most general sense.
What is unique about the pamphlet 'Cambridge Tracks in Mathematics and Mathematical Physics'?
-The pamphlet 'Cambridge Tracks in Mathematics and Mathematical Physics' is unique because it is not a standalone book but a supplement to textbooks on the integral calculus, specifically for the integration of functions of a single variable by G.H. Hardy.
Who was G.H. Hardy and what is his connection to Ramanujan?
-G.H. Hardy was a prominent British mathematician who invited the Indian mathematician Ramanujan to England to work with him. Hardy's role in Ramanujan's life is depicted in the movie about Ramanujan.
Why is 'Spherical Trigonometry' considered a strange book in the context of modern education?
-The book 'Spherical Trigonometry' is considered strange because it covers a subject that is no longer taught in schools, which makes it less common and less known to most people.
What is the significance of the book 'Origami Tree: Mathematical Methods in Paper Folding' by Thomas C. Hull?
-The book 'Origami Tree: Mathematical Methods in Paper Folding' by Thomas C. Hull is significant as it ties together a wide range of classic and modern results in origami mathematics, providing a rich historical context and becoming a standard in the field.
How did Ramanujan use the book 'A Synopsis of Elementary Results in Pure and Applied Mathematics' by George Escar?
-Ramanujan used 'A Synopsis of Elementary Results in Pure and Applied Mathematics' by George Escar as his primary source to learn mathematics when he was 16, with the help of a library copy lent to him by a friend.
What makes the book 'Counterexamples in Topology' a valuable resource for students studying topology?
-The book 'Counterexamples in Topology' is valuable because it provides a collection of counterexamples to common assumptions in topology, helping students understand the limitations and exceptions to various theorems and properties.
What is the peculiarity of the book 'Counterexamples in Analysis'?
-The peculiarity of 'Counterexamples in Analysis' lies in its presentation of various counterexamples in different areas of analysis, such as series, differentiation, and integration, challenging common beliefs and deepening understanding of mathematical concepts.
What is the comic book's approach to teaching calculus and why was it popular in the 70s?
-The comic book approach to teaching calculus, as seen in the book by Howard Swann and John Johnson, was popular in the 70s because it presented serious mathematical concepts in a fun and engaging way, inviting reader participation through suggestions and maintaining a cult following.
What advanced mathematical concepts are covered in the book by Vladimirov on functions of several complex variables?
-The book by Vladimirov covers advanced concepts such as pluri-subharmonic functions, pseudo-convex domains, domains and envelopes of holomorphy, and integral representations, which are typically studied at the graduate level.
Why is 'A Book of Curves' by E.H. Lockwood considered a unique resource for those interested in graphing?
-A Book of Curves by E.H. Lockwood is considered unique because it provides an in-depth exploration of various special curves and their geometrical properties, offering detailed instructions for graphing them, which is particularly appealing to those who enjoy graphing.
Outlines
📚 Exploring Unusual Mathematics Books
The video introduces a collection of 10 peculiar math books that span from basic to advanced levels. The first book discussed is 'The Theory of Spinors' by Élie Cartan, which delves into the concept of spinors used in quantum mechanics. The book is noted for being a Dover reprint, making it affordable. The second book is a pamphlet titled 'Cambridge Tracks in Mathematics and Mathematical Physics,' which includes G.H. Hardy's work on the integration of functions. Hardy is known for inviting Ramanujan to England. The pamphlet is described as a supplement to textbooks on integral calculus, aiming to correct the common misconception that integration relies on a multitude of disconnected methods. The video also touches on 'Spherical Trigonometry,' a subject no longer taught in schools but once considered fundamental, and 'Origami Tree: Mathematical Methods in Paper Folding' by Thomas C. Hull, which explores the mathematical aspects of paper folding.
📘 Ramanujan's Mathematical Inspirations and Counterexamples
The script continues with the story of Ramanujan, who used 'A Synopsis of Elementary Results in Pure and Applied Mathematics' by George Escar as his main resource for learning math. The book is praised for its comprehensive list of mathematical results and is available as a reprint. The video also highlights 'Counterexamples in Topology' and 'Counterexamples in Analysis,' two books filled with unusual mathematical examples that challenge common assumptions in these fields. These books are recommended for math students as they provide valuable insights into the exceptions to mathematical rules. Additionally, a comic book approach to calculus is mentioned, which was popular in the 70s and received contributions from readers, indicating its unique educational value.
📙 Advanced Mathematical Concepts and Special Curves
The final paragraph discusses more advanced topics such as 'Methods of the Theory of Functions of Several Complex Variables' by Vladimirov, which is aimed at graduate students and covers complex subjects like pluri-subharmonic functions. The video concludes with 'A Book of Curves' by E.H. Lockwood, which is a comprehensive guide to various special curves, from the familiar parabola and ellipse to the more exotic deltoid and cycloid. The book is recommended for those interested in the geometrical properties and graphing of these curves, offering a deep dive into a niche area of mathematics that is not commonly explored in modern education.
Mindmap
Keywords
💡Spinors
💡G.H. Hardy
💡Spherical Trigonometry
💡Origami Tree
💡Ramanujan
💡Counterexamples
💡Divergent Series
💡Comic Book Calculus
💡Several Complex Variables
💡A Book of Curves
Highlights
Introduction of 10 strange math books covering both basic and advanced mathematics.
The Theory of Spinors by Élie Cartan, a foundational work in the field of quantum mechanics.
Affordability of Dover reprints, making advanced mathematics accessible.
Cambridge Tracks in Mathematics and Mathematical Physics, a pamphlet supplementing integration techniques.
G.H. Hardy's work on the integration of functions, influencing Ramanujan's mathematical journey.
Spherical Trigonometry, a subject no longer taught but with historical significance in mathematics.
Raymond W. Brink's book on spherical trigonometry, offering an in-depth look at a rarely studied topic.
Origami Tree by Thomas C. Hull, connecting paper folding with mathematical methods.
Ramanujan's self-education using George Escher's 'Synopsis of Elementary Results in Pure and Applied Mathematics'.
The book 'Counterexamples in Topology', providing insights into common misconceptions in mathematical proofs.
Counterexamples and Analysis, a book with a cult following for its unique approach to teaching calculus.
The comic book format of 'Calculus and Beyond' by Howard Swann and John Johnson, blending humor with serious math.
Methods of the Theory of Functions of Several Complex Variables by Vladimirov, for advanced study in complex analysis.
A Book of Curves by E.H. Lockwood, exploring a variety of special curves and their geometrical properties.
The practical applications and historical context provided by the books for a deeper understanding of mathematics.
The importance of counterexamples in the fields of analysis and topology for math majors.
Encouragement to continue exploring mathematics and the value of these unique books for learning.
Transcripts
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