Language of the Universe

Sunday, March 16, 2014

Have Fun with Math?

(Reaction paper to our group presentation)

Who says Math is boring? EVERYONE. But things are different now. Things are awesome! Our group is awesome! Woooh! Go Group 1! Go Number System! Sorry, I get overwhelm easily. Take two. Lights, camera, action! But things are different now! Things are awesome! Math can be fun in many ways. Our group, Number System, showed some. Our group came up with a not so typical debate, a tiring and fun game, and a presentation everyone truly enjoyed.

The debate was about the existence of real numbers. Are negative numbers real? If they are, why can’t we see them? Our debate was an informal one. It tackled shallow parts only. Our goal was to present ideas that would make the audience realize that numbes are not just numbers. In the end, the debate was really about our own definition of reality. Is it limited to what our eyes perceive?

The game we had was like treasure hunting slash amazing race. Treasure hunting because of clues that lead them to each station like “Meryenda time! Saging, turon, kwek2x, atbp.” This refers to the area of Ate Saging outside CSM. Amazing race, minus the race part, because they have to go through different stations to finish the game. It was more of having points. There were 6 stations with its corresponding problem set except station 5. What’s the twist? It wasn’t only about solving and answering. It involved charades, building an index tower, cracking codes, running around, and even cheering. Yes, cheering. My station, station 5, was the hardest part according to one player. She even said, “Lou, please. Solve na lang.” Wow. That’s new. They had to make cheers for their respective groups. Don’t worry guys. I already deleted the videos. In the end, no one won. Just kidding! In the end, the winner was everyone. (char) Please claim your prizes to Mr. Quilos.

Groups	1	2	3	4	5	6	Total:
Algebra	11	6	8	5	7	10	47
Geometry	15	4	6	7	9	10	51
Statistics	13	7	8	7	9	10	54
Computer	13	5	9	7	8	10	52

Our presentation was divided into two parts. First part was compilation of videos about number systems from Egypt, Mesopotamia, Greece, China, and different bases. Our favorite was the Chinese Number system part because the numbers were taught while rapping. It was really funny. Second part was a song with Dumb Ways to Die as the tune we would present someday.

Number System everywhere

Binary, Decimal, Octal, Hexadecimal

What do they bear?

Base 2, base 10, base 16, base 8

Chorus:

Number system, the world of number system

Classification ~ of numbers in Mathematics

Egyptians uses hieroglyphics

Babylonians is in base 60

They use space for number zero

Only numbers 1 and 10 has a symbol

(Repeat chorus)

Roman uses capital letters

I, V, X, L, C, D, M

Put a line on top of the letter

To multiply the value with a thousand

(Repeat chorus)

Chinese uses the base of 10

Yi, er, san, se, and so much more

Mayan uses the base of 20

Use a line for 5 and dot for 1

(Repeat chorus)

So this is the number system

That’s all we can say

We should do our best to not forget them

Goodbye for now. See you soon!

The goal of our group was not to make fools out of everyone by making them dance in the middle of the field, but to have fun with math. Yes, it’s possible.

Cabinet of Mathematical Curiosities

This book was about the cabinet of Professor Ian Stewart with full of filings about interesting mathematical games, puzzles, stories and facts about mathematics for those people who are really much in love with mathematics. In his cabinet, you will find a lot of things that are relevant to mathematics like logic, geometry, probability and the different problems associated with math. There were also hidden keys to some theories like Fermat’s last theorem, Poincare conjecture, chaos theory and the P=NP problem.

The cabinet of Professor Stewart consists of different mystery that would test the mind of the mathematicians. Different kinds of problems tested my ability in solving while reading this book with full of mathematical computations and techniques in solving the problems. The puzzles, games and stories that include problems can be found inside the cabinet of curiosities since the unsolved problem were still hidden there, waiting for the right person to unlock the answers.

I was amazed on how did Professor Stewart collect all of these puzzles and games with answers at the end of the book. He really spend so much time in creating this wonderful math book because this would help people who are very dedicated in solving mathematical problems like those in the book. If you think of it, there are problems that can really be related to mathematical problems that would need some logic and a little bit of numbers. I think this would help us in some problems of our daily lives. We can also use this as a reference for future studies if we encounter the same kind of puzzle at least we could refer to this book.

I would also like to recommend Stewart’s book to people who have an inner ability in mathematics for them to learn more than what the others are teaching them. I would promote that this book is very exciting and you can learn a lot of things when you read it.

Rock Papers Scissors

Rock, Papers, Scissors

This book introduced and applied the concept of a Game Theory, referred to as a young science and also a study of making strategic decisions. It uses a mathematical model that they incorporate between intellectual decision makers. There are different elements of game theory that applies different strategies. The author, Len Fisher, uses experiments to perform his game that is related to the game theory and different instances in life can be explained by the game theory.

Game theories can be related to subjects like biology, politics and others where strategy can be applied because it is applicable and relevant to different subject matter. This book gives us the insights about the key ideas in game theory. The book discussed in the first chapter about the “trapped in a matrix” that describes one of the dilemmas mentioned in the book. The second chapter is the introduction of concepts about minimax and fair division. Chapter three is somehow the main topic because it discussed the “seven deadly dilemmas” that became the most interesting part of the game theory. These dilemmas are the following: Prisoner’s Dilemma, Tragedy of the Commons, Free Rider problem, Brinkmanship, Volunteer’s Dilemma, Battle of the Sexes and last but not the least Stag Hunt. The 4^th chapter was about the title itself “rock, papers, scissors” that can be used in resolving conflicts in the game by using strategies and resembling it to the “rock, papers, and scissors” game situation. While the chapters five to eight were all about collaboration or cooperation with science.

Reading this book taught me the different strategic decisions about life and introduction of real-life game theories. I would recommend this book to everyone for them to have an idea on how to achieve trust and change our life’s game to escape the dilemmas and unwanted consequences in playing your life’s game theory. I can say that the author had a great job in introducing the Game Theory.

Algebra individual report

Algebra

Algebra is said to be a generalized arithmetic and these numbers were organized and strategized from the original concept. All mathematicians used algebra to derive the different formulas that they have discovered and so you cannot jump into your derivation without passing through the concepts algebra. This branch of mathematics was first used to solve some theories of equations and was said to be originated from the Babylonians but the word algebra came from the Arabic word Al-jabr from the book of Al-Khwarizmi, and was later utilized by the other mathematicians.

I think I somehow learned something from algebra from its basic concept that can be strategized into a new equation following some patterns that was seen in an equation. There are different types of algebra around the world like the Babylonian, Egyptian, Greek geometric algebra and more. Learning algebra is not just about solving and computing equations but deriving the formulas from the patterns seen in a solution that is why mathematics is all about patterns that can be generalize to create applications in the real world.

I can say that algebra is really a big help in taking higher math because we will first learn from the basic steps before jumping to its applications. And I learned some of its parts like the linear equations, graphs, relations, functions, word problems and its connection to consumer mathematics. Learning math is not difficult you just have to love and appreciate it whole-heartedly for you to enjoy and value its importance to the real world applications. Our group created a mini game that will test the players solving ability given a problem and some concepts behind the mathematical theories.

I learned that even though mathematics, algebra in particular, has different theories; they are somehow related because the process of deriving their ideas passed through the basic concepts of algebra. If you come to think of it, algebra is just a combination of numbers, mathematical signs and an unknown variable. You just need to play with these ingredients in order for you to attain the right equation to the problem. We just need to utilize the learnings that we obtained to create a new mathematical history that would be an advantage in the mathematical world. Appreciating math is the first step in loving the wonderful philosophies of mathematics plus the curiosity to patterns would make you think deeper.

Computers

A Reaction Paper to the group report

Reaction Paper to Group Presentation

Group 5: Computer

At the beginning, when choosing a sundry topic per group, personally I really first thought of computers is the easiest among the five. Only to figure out that it was not that easy to construct a game, a presentation and a debate all about computers.

I do believe that prepared mind is favored by chances. In our case we really didn't have the chance to prepare and organize orderly our presentation as a group. Though we were the last group to report, having the longest time to think hard and prepare but I guess we really did miss to cooperate and work as a group.

In our presentation, we role play a TV show in wherein a computer analyst was interviewed for her exhibit of the different computers. In the exhibit, it showed the generation scheme of the development of this powerful programmed machine. Even though, the said presentation was kind of boring and not that entertaining but the content of the history of mathematics was laid.

In our debate, we discussed about the negative and positive effects of the computer. The affirmative side believes that the computer has brought the users to some points of addiction, as cite of crime such as plagiarism, identity theft, cyber sex and libel. On the other hand, the negative side strongly believes that the computer had really been a great helpful and useful device to the entire world that has been using it now. Without it a lot of things could not be possibly done. This mathematical device that had only started to be used in calculations and researches had now a lot of variety it has to offer. It had gone variously in several purposes. One thing cannot be deny is that this machine that functions in many various ways had helped us in every possible way it can. Thus the computer had brought progress to the technological world. And the effects of computer only depend on the person behind the screen.

I can say that this device is one of the world’s renowned possession and discovery that the future generation would always be thankful to the persons behind the innovation of the single chip to the complex computer we are using right now, and maybe in the future there could be more to that.

The Thing That Changed Everything

Who on earth does not know about computers? From a pre-schooler who thinks that computers games are way much better than street games where you get dirty and all to an elder who takes a picture of her medicine before taking it, uploads it in facebook with a caption, "Time to take my medicine (sigh)". Almost everyone uses it!

The rise of computers had make our lives completely different. The current developments in each areas of the society (like health, politics, education, etc) are due to computers. It is the one who made our society modern. Before we discussed more about it, let us take a look on its history first.

This essay would not be enough to tell the complete history of computers. So as to make it short, I will focus on the five most significant generations on the timeline of computers.

First generation began in 1946 when the ENIAC system became operational. ENIAC stands for Electronic Numerical Integrator and Calculator and was built by the University of Pennsylvania. ENIAC is the significance because it is the first general purpose electronic computer system and also it was used for research, not commercial applications. It operated using 18,000 vacuum tubes and could perform 500 basic arithmetic functions per second. Then, UNIVAC followed, the first machine purpose-built for commercial electronic data processing.Like ENIAC, it still operates using vacuum tubes but it is better because it is capable of handling numeric and alphabetic information equally well.

Second generation would involve transistors. They were available commercially in 1959. They are much smaller than vacuum tubes, have greater reliability and use less power. The third generation came and transistors were replaced by silicon ships.Time came when the number of circuits that can be packed into a single chip (several hundred thousand on each). This was the fourth generation.

Lastly, the fifth generation involves computers that process data with light pulses instead of electrical pulses.

The second purpose of this entry is also to mention other types of computers we encounter in our daily lives. Many had thought that the word computer only refers to the laptops and personal computers used in offices, homes and school. However, it is just one type of computers. From the latest alarm clock that wakes you every day to the automated shower that you used before going to sleep. Most people might not realize that those products have microcomputers inside. They are operated by wires and chips same to the wires and chips also used in computers.

Thirdly, I would like to state the roles of computers in our society. Because of them, many inventions on the newest machines that diagnosed people of their sickness has arise in the medicine section. We had the famous CCTVs which are used at homes, offices and even in schools that are very useful for solving crimes. Communicate overseas is now possible because of them and many more.

In conclusion, those examples, which I mentioned above, shows that computers play significant roles in our society. It can be said that our modern lives cannot exist without computers. Even though computers participate actively and play more and more important roles in our world, they are still one of the useful tools for human beings so far. And seeing of how they are developing everyday, it is difficult to imagine how these computers would be hundred of years from now.

A Cabinet Full of Wonders

“What is more interesting than reading a book of mathematical problems and puzzles?” These were the exact words that formed in my mind while I was reading Ian Stewart's book entitled "Cabinet of Mathematical Curiosities".

The book started back when he was still 14 years old. He used to keep notebooks where he wrote all the interesting things about math that wasn't taught in school. It started in one and then, without him knowing it, he became very engaged to it that it became 6! These became the famous Professor Stewart's Cabinet of Mathematical Curiosities who opened its drawers and revealed a superb collection of games, puzzles, stories, jokes and factoids, odd items of mathematical culture, card tricks, things to make and things to do! You will also learn why M25 is shorter than clockwise, which can be incorporated with Fermat's Last Theorem, the chaos theory, fractals, and Penrose patterns, and the reason behind why can't you divide any number by zero.

What's really amazing in this book is that it is the only book that does not focus on a story, it has no moral, no parable and no lengthy words to convince us that mathematics is awesome. It convinces its readers through mathematical games and puzzles. Amazing isn't it?

The question now is, did I read every word? Did I solve every problem? My answer would be no for both. Honestly, I am the type of reader who only wants to read what is the most interesting parts of the story. I'm not really into those lengthy words with a lot of flowery words that bores me to death. I also tried answering some, luckily I got right for some items, but when I couldn't solve 5 items in a row, I stopped and just continued reading the book and then afterwards realized how easy it was to solved.

I really recommend this book to everyone especially to those people who despised solving mathematical problems because I really assure you that this book would not only entertain you with its games and puzzles but as well as teach you that mathematics beyond school isn't that bad after all. Then maybe, just maybe, you could become the next Ian Stewart and begin your own cabinet that is full of wonders.

every interesting thing he could find out about the maths that wasn’t taught at school - See more at: http://www.bookstok.com/books/details/book-professor-stewarts-cabinet-of-mathematical-curiosities-1846683459-7198#sthash.0QwoiekW.dpuf