Javier A. Tabush

Joy of X

Chapter 1: FROM FISH TO INFINITY

• I really liked this introduction from the author since he approaches mathematics in a different way, as Aristotle would say he approaches it like a stranger

• I also like how we approaches everything with questions

• “Where exactly do numbers come from? Did humanity invent them? Or discover them?

• This actually helps the reader to connect with the book and enjoy more the experience

Chapter 2: ROCK GROUPS

• He explains us the basic first steps of mathematics and he uses rocks in order to represent them

• He also teaches us the different operations that math has using the rock and showing us how divisions and fractions work

• “Looking at numbers as groups of rocks may seem unusual, but actually is as old math itself. The word “calculate” reflects that legacy, it comes from the Latin word calculus, meaning pebble used for counting”

Chapter 3: THE ENEMY OF MY ENEMY

• “Subtraction forces us to expand our conception of what numbers are”

• I liked how he states that we are all afraid of subtraction due to the fact that subtraction can produce negative numbers, and nobody likes negative numbers.

• He uses stories that are parallel to what he’s talking about in the chapter, in this case subtraction, and that’s why he calls it “the enemy of my enemy”

• “By sorting the meaningful from the generic, the arithmetic of negative numbers can help us see where the real puzzles lie”

Chapter 4: COMMUTING

• In this chapter he explains how every decade or so new techniques appear for teaching math. Which I feel is totally true because I remember when I was in school and I asked my dad for help in my math homework we both had different ways to approach and solve the problem.

Chapter 5: DIVISION AND ITS DISCONTENTS

• “There’s a narrative line that runs through arithmetic, but many of us missed it in the haze of long division and common denominators. It’s the story of the quest for ever more versatile numbers”

• As I get more into this book I like it more and more because he treats the reader as if he/she didn’t know anything about mathematics, so he makes everything appear much easier than it actually is.

• “Fractions always yield decimals that terminate or eventually repeat periodically, that can be proven, and since this decimal does neither, it cant be equal to the ratio of an whole numbers, its irrational.

Chapter 6: LOCATION, LOCATION, LOCATION

• He talks about the legacy that Babylonians left us.

• It’s amazing how much we can learn by asking ourselves different questions about the past, but we never do it, because we live in a culture where people don’t actually care about the legacies that old generation have left us.

“But the greatest legacy of the Babylonians is an idea that’s so commonplace today that few of us appreciate how subtle and ingenious it is” BINARY NUMBERS

Chapter 7: THE JOY OF X

• At the beginning of the chapter he tells us that “its time to move from middle school arithmetic to high school math”

• Variables, division of algebra and units.

Chapter 8: FINDING YOUR ROOTS

• “For more than 2500 years, mathematicians have been obsessed with solving for x. The story of their struggle to find the roots, the solutions, of increasingly complicated equations is one of the great epics in the history of human thought”

• He starts to mention the imaginary numbers and how i can never be found

• “In 1976, mathematicians were still searching for roots, but now the instructions were written in binary code”

Chapter 10: WORKING YOUR QUADS

• The Quadratic formula!!!! AHHHHH, I’ve always been afraid of it.

• What is so remarkable about this formula is how brutally explicit and comprehensive it is.

• The quadratic formula has become an irreplaceable tool for practical applications. Engineers and scientists use it all the time

Chapter 11: POWER TOOLS

• Parabolas and constants

• They are both associated with power functions of the form x to the power of n

• What is exponential growth?

• “In theory, exponential growth supposed to grace your bank account. If your money grows at an annual interest rate of r, after one year it will be worth 1+r times your original deposit”

 

Chapter 12: SQUARE DANCING

• The author tells us something that is very true, most of us really liked geometry when we were in high school because it was on the least things we truly understood concerning to mathematics.

• When approaching the Pythagorean theorem he truly wants to understand why is it that it is that way.

• He explains to us how the two triangles make a square and that’s why all of the variable are squared.

Chapter 13: SOMETHING FROM NOTHING

• “Every math course contains at least one notoriously difficult topic. In arithmetic, its long division. In algebra, its word problems. And in geometry, its proofs”

• When I read this chapter there was one quote that struck me so much because of the meaning it contains and how it connects to other texts we have read at the MPC

• “Issac Newton channeled Euclid in the structure of his master work Principles of Natural Philosophy. Using geometrical proofs he deduced Galileo’s and Kepler’s laws about projectiles and planets from his own deeper laws of motion and gravity”

Chapter 15: SINE QUA NON

• In this chapter he focuses more on charts and how important they are for representing information about a certain topic.

• One topic that I really enjoyed reading about and I thought I was going to hate it was the topic about WAVES, specifically sine waves

• “Sine waves are the atoms of structure. They are nature’s building blocks. Without them there would be nothing, giving new meaning to the phrase “sine qua non”

Chapter 16: TAKE IT TO THE LIMIT

• If you keep moving halfway to a wall, will you ever get there?

• It was really funny when he said that questions like these ones cause headaches and that makes it much harder for us to approach them.

• How do we know that pi is the same number for all circles?

• Could it be different for bigger circles and for smaller one?

Chapter 17: CHANGE WE CAN BELIEVE IN

• The first approach to calculus!!! Scary

• I’ve never been that interested in calculus but now I see that calculus is everywhere. And whenever I heard the word “derivative” I completely got dismotivated and stopped trying

• But now I know that “the derivative tells you how fast something is changing”

 

Chapter 18: IT SLICES, IT DICES

• “Mathematical signs and symbols are often cryptic, but the best of them offer visual clues to their own meaning. The symbols for zero, one and infinity aptly resemble an empty hole, a single mark, and an endless loop”!! HOFSTATER!!

• Before calculus, change couldn’t be calculate as good as we can do it now.

• When something changes steadily, at a constant rate, algebra works beautifully!!

• The fundamental theorem of calculus says that if you integrate the derivative of a function from one point to another, you get the net change in the function between two points.

Chapter 20: LOVES ME, LOVES ME NOT

• I really liked how he uses the analogy of Romeo and Juliet to explain the differential equations, something that is not so easy to understand, but somehow the author manages to do so in a very fun and dynamic way.

• “In the nearly 350 years ago since Newton, mankind has come to realize that the laws of physics are always in the language of differential equations. This is true for the equations governing the flow of heat, air, and water; for the laws of electricity and magnetism; even for the unfamiliar and often counterintuitive atomic realm, where quantum mechanics reigns”

• It’s amazing the amount of connections that this book has with the rest of the curriculum.

Chapter 22: THE NEW NORMAL

• “Statistics has suddenly become cool and trendy” I loved this quote, the first sentence of the chapter.

• This chapter talks about statistics and how is probability useful in our daily lives

• This is why I am loving this book, because it has real life applications of all the branches of mathematics that he talks about throughout the text.