The Library
Just like how a musician needs his instrument, or a basketball player needs his sneakers, I believe as a mathematician, he should have his own arsenal of books. Need a way to solve a differential equation, he can turn to his trusted Calculus book. Or maybe the real plane isn't enough for this current situation, he will then look up on some complex plane definition. I, for one, take pride in my collection of mathematics books. Not only do they set the course for my endeavour into the world of all numbers, they also plant the foundation of mathematics - the multitude of theories and principles that have stood the test of time.
While I could have simply extracted thumbnails from Amazon.com to show you the covers of the books, I took the liberty to pose myself with the books. You seen, I do not look at my books as lifeless pieces of paper waiting to be withered. Instead, I view them as living entities, entities which can't wait to pass the knowledge of mathematics to those who are willing to open them.
My recreational
and utility mathematics book. This book is aimed to train those who wish to participate in the American Mathematics Competition. While it does have its fare share of exercises and problems, this little book manages to contain almost all the high school math topics neatly presented through precise theorems and definitions. Using it for a while now, this text has been a source of either a quick reference or simply just some good old AMC fun.
Favourite Chapters:
Polynomials and their Zeros
Sequences and Series
Complex Numbers
In line with the title of this book, this marvelous gem chronicles the life and work of five giants in the world of science and mathematics. After Stephen Hawking gives a honorary introduction these great people, the book reveals 5 historical publications: 'On the Revolution of Heavenly Spheres' by Nicolaus Copericus, 'Dialogues Concerning Two New Sciences' by Galileo Galilei, 'Harmonies of the World Book' by Johannes Kepler, 'Principia' by Sir Isaac Newton, and 'Selections from the Principle of Relativity' by Albert Einstein.
With each text, a refreshing revision is given where the language has been updated to suit that of modern day while still maintaing the original interpretation. In addition, the graphical images and drawings which illustrates the various concepts are simply appealing. Most of them are computer generated renderings which breaths new life into these old works.
While difficult to understand, I have adopted an attitude of diligence in comprehending this book through multiple readings.
Favourite Chapters:
Principia
One of the many classic books under the famous Dover Publications. This book existed solely for the purpose to shed some light on the subject which I consider most difficult, Group Theory. This book is written in a rather old fashion where less attention is paid to the paragraphing and more attention is paid to the substance of the topic. I personally like it this way as I would rather be bombarded with theory after theory when studying a more abstract topic like Group Theory.
Given its small size, I usually carry it around with it during my short rides on the bus.
Favourite Chapters:
Irreducible Representations (very hard)
Applications Involving Algebraic Forms (even harder)
My trusted Complex numbers reference book. This book serves as a good one-term introductory course to the theory and applications of functions of a complex variable. After going through the material, it allows the reader to go off into his own tangent to prove the more difficult theorems in complex numbers or in other fields like analysis.
The first few chapters forms a smooth transition from high school mathematics to undergraduate level complex numbers. As I work more on the book, I personally like the style of author of how he starts with theory and concepts and towards the end, moves more to applications. It is a delight to see how problems in physics such as fluid flow and steady temperatures are treated with complex numbers.
Lastly, it contains a rare proof of the Fundamental Theorem of Algebra.
Favourite Chapters:
Residues and Poles
Conformal Mapping
The Schwarz-Christoffel Transformation
"Mathematical disputes offer indisputable proof that great mathematical minds are calculating in more ways than one."
For anyone who wishes to know about the stories behind the multitude of theorems in the realm of mathematics, this book proves to be a good read. It showcases ten of the most famous disputes between the great mathematicians since the 17th century. Was it Tartaglia or Cardano who won the battle of solving the first cubic equation. How did a humble discovery of the calculus cause a rift between England and Germany.
Hellman does a wonderful job in bringing life to the history of mathematics. After reading the book, one can't help but think that mathematicians are after all, not 'boring' people who do nothing but create theorems. Instead, we see that they are people of academia, driven and passion of the one thing they believe in, finding mathematical solutions to every problem and in doing so, progress the science to another level.
Favourite Chapters:
Newton versus Leibniz
Beroulli versus Bernoulli
Poincaré versus Russell
Out of the twenty General Relativity books I saw on Amazon, I decided to go with Hartle's one and it was good choice.
To the uninformed, and let me try my best to explain this, General Relativity deals with the concept of separate frames of reference having their own scale of time and that this scale actually changes with respect to gravity. Understanding the above line requires knowledge in a few topics but thankfully, this book manages to effectively teach the required concepts namely, differential geometry, spacetime diagram and principles of relativity.
I try to make it a point to study at least a chapter every Sunday, hoping to build up my knowledge of all these non-Newtonion terms. After a few weeks, I have only one statement to say regarding the subject: General Relativity is hard. I believe the main reason to be that GR throws out your four years of high school physics and builds on a new foundation, one where time is made to vary. My advise, if you want to be a professor in GR, study early.
Favourite Chapters:
Special Relativistic Mechanics
The description of Curved Spacetime
Just like how a musician needs his instrument, or a basketball player needs his sneakers, I believe as a mathematician, he should have his own arsenal of books. Need a way to solve a differential equation, he can turn to his trusted Calculus book. Or maybe the real plane isn't enough for this current situation, he will then look up on some complex plane definition. I, for one, take pride in my collection of mathematics books. Not only do they set the course for my endeavour into the world of all numbers, they also plant the foundation of mathematics - the multitude of theories and principles that have stood the test of time.
While I could have simply extracted thumbnails from Amazon.com to show you the covers of the books, I took the liberty to pose myself with the books. You seen, I do not look at my books as lifeless pieces of paper waiting to be withered. Instead, I view them as living entities, entities which can't wait to pass the knowledge of mathematics to those who are willing to open them.
First Steps For Math Olympians by J. Douglas Faires
Favourite Chapters:
Polynomials and their Zeros
Sequences and Series
Complex Numbers
The Illustrated On The Shoulders of Giants by Stephen Hawking
With each text, a refreshing revision is given where the language has been updated to suit that of modern day while still maintaing the original interpretation. In addition, the graphical images and drawings which illustrates the various concepts are simply appealing. Most of them are computer generated renderings which breaths new life into these old works.
While difficult to understand, I have adopted an attitude of diligence in comprehending this book through multiple readings.
Favourite Chapters:
Principia
Symmetry An Introduction to Group Theory and Its Applications by Roy McWeeny
Given its small size, I usually carry it around with it during my short rides on the bus.
Favourite Chapters:
Irreducible Representations (very hard)
Applications Involving Algebraic Forms (even harder)
Complex Variables and Applications by James Ward Brown and Ruel V. Churchill
The first few chapters forms a smooth transition from high school mathematics to undergraduate level complex numbers. As I work more on the book, I personally like the style of author of how he starts with theory and concepts and towards the end, moves more to applications. It is a delight to see how problems in physics such as fluid flow and steady temperatures are treated with complex numbers.
Lastly, it contains a rare proof of the Fundamental Theorem of Algebra.
Favourite Chapters:
Residues and Poles
Conformal Mapping
The Schwarz-Christoffel Transformation
Great Feuds in Mathematics, Ten of the Livelist disputes ever by Hal Hellman
For anyone who wishes to know about the stories behind the multitude of theorems in the realm of mathematics, this book proves to be a good read. It showcases ten of the most famous disputes between the great mathematicians since the 17th century. Was it Tartaglia or Cardano who won the battle of solving the first cubic equation. How did a humble discovery of the calculus cause a rift between England and Germany.
Hellman does a wonderful job in bringing life to the history of mathematics. After reading the book, one can't help but think that mathematicians are after all, not 'boring' people who do nothing but create theorems. Instead, we see that they are people of academia, driven and passion of the one thing they believe in, finding mathematical solutions to every problem and in doing so, progress the science to another level.
Favourite Chapters:
Newton versus Leibniz
Beroulli versus Bernoulli
Poincaré versus Russell
Gravity An introduction to Einstein's General Relativity by James B. Hartle
To the uninformed, and let me try my best to explain this, General Relativity deals with the concept of separate frames of reference having their own scale of time and that this scale actually changes with respect to gravity. Understanding the above line requires knowledge in a few topics but thankfully, this book manages to effectively teach the required concepts namely, differential geometry, spacetime diagram and principles of relativity.
I try to make it a point to study at least a chapter every Sunday, hoping to build up my knowledge of all these non-Newtonion terms. After a few weeks, I have only one statement to say regarding the subject: General Relativity is hard. I believe the main reason to be that GR throws out your four years of high school physics and builds on a new foundation, one where time is made to vary. My advise, if you want to be a professor in GR, study early.
Favourite Chapters:
Special Relativistic Mechanics
The description of Curved Spacetime
