Strategic Decision Making

A review on Rock, Paper, Scissors by Len Fisher

Note that the book is not about how to win the typical rock, paper, scissors game; as the reader may think from reading its cover. This book covers the other side of game theory, the study of strategic decision making. Game theory has been widely used to explain patterns of behaviors in various sciences and on how we can maximize our gain in situations of conflicts and competitions.

The book has a slow start, beginning with chapters that talk about the Prisonner's dilemma and Nash equilibrium concepts, which would appear to be a logical trap. Nash equilibrium can be created when both parties favours each of their self-interest, leading to many dilemmas and problems in our society. Also, Len Fisher discusses the limitations of game theory: “What’s best for you isn’t always what’s best for everyone else”. A concrete example is when you throw garbage on the street rather than on a trash can. If everyone else would do that, our streets would be full of trash and pollution would be all over.

It’s funny how the game “rock, paper, scissors” is played in every part of the earth. At the same time, it is used in resolving conflicts for the reason that this game has no actual strategies for one side to dominate the other. Hence, scenarios and games which seem to be a dead end can be solved through adding strategies and making them the same situations as rock-paper-scissors.

In spite of competitions, cooperation within people can be achieved to change the game and so we can avoid the traps leading to unwanted outcomes. This was discussed in the succeeding chapters; however the major points were similar to the nature of narratives from the previous ones, with interesting examples from science.

I’d like to think that the most significant part of the book is the “Notes” section, which was saved for last. I had fun reading with the narratives, jokes (though some were corny) and random trivia. Because of this, I therefore consider the book to be worth reading. The author’s style is smooth, a little bit humorous and easy to comprehend. Plus, he writes based on his past experiences which I, as a reader, can totally relate. If you want to learn about game theory quickly and you want it interestingly, this book might be what you’re looking for.

Choices and Decisions

Choices and Decisions

A Book Review on Len Fisher’s, “Rock, Paper, Scissors: Game Theory in Everyday Life”

            First of all, I just want to say that the author, Len Fisher, has been very considerate in writing this book because he wrote it in a manner that is not entirely mathematical and is short but was still able to depict everyday circumstances in which we may have overlook the game theory playing on the sidelines. If you are looking for a good read about strategies on gains, negotiations or deals, or just simply yearning to understand how a situation may result in two or more parties, then, this is the book you are looking for. Written in a light manner, Rock, Paper, Scissors, is a comprehensive and relatable read.

           

            Fisher shows the positive effects of cooperative behavior in certain difficult situations as well as escaping traps set by selfishness. Not many people are willing to cooperate voluntarily. Cooperation may be easy to do once a party is convinced that there is something good in store for them. However, if one person is not so good with arguing, or perhaps devising compelling bargains, what good would be in store for both parties? No deals may probably happen. Thus, the seven deadly dilemmas have been enumerated to help us understand the logic behind situations usually leading us to social dilemmas. These seven deadly dilemmas are as follows: the prisoner’s dilemma, tragedy of the commons, free rider, chicken, volunteer’s dilemma, battle of the sexes, and the stag hunt. Among these mentioned, the most common dilemmas that I see in daily living are the free rider, chicken, volunteer’s dilemma, and the battle of the sexes. The seven deadly dilemmas might appear as just simple things. However, what we sometimes fail to see is that big things come from small beginnings because the applications of these dilemmas range from interpersonal relationships to global issues and connections. It is especially hard to make a wrong move in the global scale --- war may result from it.

            Many, if not all of us, go into conversation with other people by, say, for example, congregating, making bargains &/or deals, fixing time meetings, making state treaties, simply arguing who will pay which in dining hangouts (or if it would be equally divided), etc --- same conversations over and over again. But the manner of how we plan certain things so as to suit ourselves positively varies. We may be or not be good in looking into the future. I, personally, have found a connection with some of the simple, daily examples of the dilemmas in the book. I do not know if I would use the logic behind them in the near future to escape traps, too. One thing is for sure, I have somehow understood how one’s selfishness can control just about everything the person would do, most especially the words that would come out of their mouths. The good thing is that there are ways to counteract such behavior(s). Learning how to play the game effectively is the answer.

Arrows and Ladders: A Narrative of the Algebra Presentation

In a Math1 class, students are divided and grouped according to different topics of mathematics. Each group is tasked to facilitate a game, a debate, and a creative performance with regards to their assigned topic. Me and my groupmates were assigned with the topic of Algebra. Well, more like we aggressively picked Algebra. Hehe.

Each group was given two meetings for presentation. We spent the first day for the game. Our game was snake-and-ladder - arrows-and-ladders style. Each player (the remaining groups) is given a chance to roll a dice. After then, they would have to answer a question based on Algebra, which I was assigned to come up with. They would move forward according to the number indicated on their rolled dice if they answered correctly, otherwise, they would have to stay on their previous spot. The team that would get the highest score or the farthest spot is the winner.

For the second meeting, we had a debate on the topic, "In theory, division by zero is possible." After preparation, we presented our debate and I was on the negative side. We ended the meeting with a group performance by singing songs on slope-intercept (to the tune of 'Good Girls Go Bad' entitled y=mx+b) and studying math (to the tune of 'The Lazy Song'). We also presented videos and a humorous love story concerning maths.

The presentation was really fun and everyone enjoyed it. This just shows that anyone can have fun with Algebra, or maths, in general. Maths is part of our daily lives. We should realize and appreciate its importance as it makes our life meaningful and convenient.

The Frontiers of Space - movie review

“The Frontiers of Space” is the third episode of the series of the Story of Maths brought to us by Prof. Marcus du Sautoy from Oxford. This episode presented us various mathematicians which focused on the development of mathematics in Europe around 16-19^th centuries up to what and how it is being used today.  Around 17^th century, Europe was able to overpower and replace Middle East in becoming the world’s engine house of mathematics ideas.

It was shown in this episode how mathematics helped illustrating a 3D perspective in a 2D representation. Another is, connecting algebra and geometry was remarkable discovery. Usage of numbers, wherein formulas where deducted, in correlating exact values or defining shapes and figures made mathematics more precise and easily predictable. In addition, curved lines were described using equations. It was also presented how codes helped in protecting our credit card transactions in the internet.

One amazing part in this episode is the presentation of Isaac Newton’s contribution to mathematics. People actually never knew his contribution/s in this field, even those people who wander in the area where he lived. Newton actually discovered significant mathematical ideas, particularly the development of calculus where at the same time a rival also did the same, Leibnitz. The development was crucial to understanding the characteristics of moving objects. In addition, Professor Marcus mentioned the father of topology, Leonhard Euler and Gauss who invented a new way of handling equations which is modular arithmetic. Furthermore, it was shown how Riemann studied behaviors and properties of objects.

Y=mx+b

            I was a part of the algebra group. I was happy that we got the topic Algebra because I think it was easy. It is the basics of mathematics so it really was easy. Also, students tend to forget the basics but these basics are very useful in order to answer the questions in higher mathematics. Maybe my group mates were not that comfortable in Algebra, but I am. And I think being assigned in this topic would not only make us but also the whole Math 1 class bring back their knowledge of Algebra and appreciate the basics again.

            First we conducted the game named “Arrows and Ladders”. This game was a modification of the popular game snakes and ladders. Each group would take turns in rolling the dice. If they are able to answer the question given to them (which is algebra related) they could move forward. The group that would get the farthest block would be declared as winner.

            The next meeting, we did a debate entitled “In theory, division by zero is possible”. We chose this topic since it is very interesting. If this theory is true, then it would be mathematically possible to say 1=2. Two of my group mates were on the Negative side while I and my other group mate were on the affirmative side. I was glad we chose that topic because our classmates were able to understand the arguments in there. This only shows that they know the basic which is algebra.

            Next is we performed our creative presentation. I was assigned to think of these creative presentations. It was hard. Initially I was thinking that we would perform the history of algebra. We’d create a play. But it would be hard to practice since our schedules are all conflicting since were in different courses and year levels. So I used the youtube video I saw about the slope-intercept. The lyrics were sent to my group mates so that they would be able to practice the song.

We showed videos related to algebra as well as that video showing to nerd lovers using mathematical terms in showing their love for each other. Then we performed the jingle “y=mx+b” which was really fun and also made our classmates enjoy and laugh.

            This just shows that even though a lot of students don’t like algebra, it is very useful. A lot of the things in our surrounding have algebra in it. We just can’t see and appreciate it because it is the basics the “roots” hidden below. 

                MOVIE REVIEW: To Infinity and Beyond

Another instalment of the Story of Math, this time we focus on modern-day mathematics, its mathematicians, equations and its philosophies.  A German mathematician named David Hilbert. He proposed 23 mathematical problems and these problems would be core findings on modern day mathematics. George Cantor amazingly understood infitinity, at first the concept of infinity was confusing and it was very hard to grasp the full concept, but Cantor fully understood its notion, infinity isn’t just in whole numbers but in fractions, that there lies infinity inside two normal numbers. He understood on what to be an impossible concept, mathematicians have this innate ability to think outside the box, to really dig down on the complex understandings on which normal humans cannot fully understand. Like the description, Poincare would understand complex mathematics and was very good at it. Even though he wasn’t working his subconscious would do the work for him. An amazing skill that no normal being can do, this led to his findings about the different orbital paths of multiple heavenly bodies. This also led to the widely known and very interesting theory as the chaos theory on which tiny changes can have huge amounts of effects.

                The concept of topology is quite simple. Basically its bendy geometry, in which 2 shapes are the same if you can morph one to another without cutting it. One mathematician named Perelman, understood well on the dynamics of shapes, looking at possible ways that three-dimensional shapes can be morphed. Perelman is quite humble, he would better be out solving mathematical problems rather than acquiring awards and recognition, a core behaviour that would apply to all mathematicians.

                Hilbert believed that mathematics was the key to understanding concrete truth and a tool to achieve certain knowledge. He declared that unsolvable problems did not exist and anyone and everyone can solve it. His saying goes “We must know, we will know” was  key for mathematicians on solving their problems, that there is no reason on why they solve problems but finding out the absolute truth.

                Godell had a unique perspective on mathematics, quite opposite of that of Hilbert. His Incompleteness Theorem spearheaded the foundations of logic and reasoning, it would turn out that you would have an answer but cannot be proven. After the Nazi regime mathematicians and scientists were silenced, not much discoveries were found. Even Hilbert was taken in with the wrath of the Nazis. After this the mathematical baton was given to the East.

                On the new world, different mathematicians on the east were interested in old mathematicians work such as Cantors Continuum Hypothesis which was proven by Paul Cohen. There were even female mathematicians, most of them fled from Nazis, they had potential. Then the first ever woman to be ever elected as the president of the American mathematical society, Julia Robinson. She was a strange and different kind of girl, she was mostly alone and at an early age had a quirk for numbers and patterns. Julia was famous for her Robinson Hypothesis in which he took up Hilbert’s 10^th problem.

                Robsinson could not solve this problem until a Russian mathematician named Yuri Matiyasevich solved it when he was just 22 years old. But he wasn’t the only young mathematician, Galois was only 20 years old when he died but he developed Algebraic Geometry, how mathematical equations and structures can be used in geometry, algebra and topology. Even greater mathematicians such as Nicholas Bourbaki published great amount of works, but Bourbaki was actually a pseudonym for a group of French mathematicians. Grothendiek viewed mathematics differently and understood it in its most fundamental ways, that basic understandings could solve complex problems. But Grothendiek turned his back against mathematics and chose politics. A sad loss for mathematics, nowadays only there are only few that has the passion and ideals for solving mathematical problems. In previous instalments we explained that mathematics has a huge effect on technology, the more complex the mathematics is the more significant it is to practical application. The ultimate purpose of math is to find truth; removing any uncertainty and finding absolute reality.

X+Y=Z

Reflection on Algebra

When were grouped and designated to choose a key topic pertaining to the lessons that will be discussed in Math 1, I then felt I’ll be having a bad time. Algebra was our chosen topic to be presented in the class. It’s not that I don’t like this nor love it, but I believe there were other more interesting (or easier) topics to choose from. Why this one of all? And why was I so hesitant to agree with my fellow group mates to pick this topic? Algebra is fundamental and that’s what makes it appear slightly hard to me. Because when you go on and take advance mathematics, you sometimes forget the basics.

What we did was a game called “Arrows and Ladders” where we customized the typical Snake and Ladders game everybody knows. To play the game, one must answer the problems algebraically. Like playing snake and ladders, they would roll a die first. If they can answer the corresponding problem given (related to algebra of course) and provide the necessary calculations and solutions, then they may move forward (nth times depending on the result of the die rolled) until they land on another block. The group that reached the finish point (block) first was considered to be the winner. We wanted everyone to cooperate within their groups and engage in a friendly competition among other groups. Also, we wanted them to enjoy the game and enjoy algebra.

In our group, we had a division of labour since we all have busy schedules and our free time would not match to one another. I was in charge in preparing the script for our debate and it took me really long to contemplate on what algebraic concept we should argue on. In the end, we decided to take on a mathematical debate that would use algebraic skills to discuss on. The topic adopted was “In theory, division by zero is possible”. There were only four of us so I had to play the part of a moderator and at the same time, defend on the affirmative side.

Next, we showed videos to the class regarding algebra, its applications and importance. We performed a jingle entitled “y=mx+b” which was about solving linear functions. I think our classmates enjoyed our presentation, since I’ve seen it in their wide smiles and laughers.

As for my reflection, algebra is one that many people mumble as to why be it important for learning. I’ve encountered many saying from friends and classmates like “Why do we always need to find this x anyways?”; “Can I say, I would like to buy x⁴⁵+890x³³-12.45x^-1 kilo of apples when buying in the market?”; “Will I be able to use all of these equations in my everyday life?”. To answer their question, here’s my realization: I can live without algebra, but I will not appreciate much of the things surrounding me. I might not be eligible for the course I am taking right now. I will not be able to participate fully in our technological society. I'll be more likely to make unwise decisions and find myself with less control over my life than others who have this knowledge. Yes, I will live in the same world with them, but I would not see nor understand as much of the beauty, structure and mystery of algebra. And, I will not have as much fun!

Math Is A Wonderful Thing

This is the first time I’ve encountered a novel entirely about math. Sure, there are novels inspired by math, but this one is entirely math from beginning until end. The authors have taken a new and quite interesting approach of conveying math to the people. They deviated from what scholars like them usually do; construct a book with hard facts and highly technical terms that make your brain bleed out and just want to close the book. Because let’s face it, you would rather read a fiction book than a non-fiction book. So, the idea of incorporating math and a novel is genius because they not only piqued the interests of the general readers but also express their message in an imaginative and understandable way.

The book is about an Indian named Ravi, a student who lost his passion for math with his grandfather’s passing when he was a boy. Through the course “Thinking about Infinity”, his professor Nico Aliprantis, and old records of his grandfather he uncovered, he regained his interest for math; in a way fulfilling his Bauji’s wish for him. The narrative of the story is pure fiction, but the mathematics is entirely true. The book encompasses infinity, set theory, Euclidean and non-Euclidean geometry, and other fields such as philosophy and religion. The authors have done a wonderful job in making the mathematics easy to understand (and with visual aids) for the benefit of the readers.

What I liked best about the novel was that, for once, it did not make math boring. It was actually a page-turner and very educational. Since it’s a combination of fiction and non-fiction, I saw mathematics in a different light. For me, it’s like Dan Brown’s Robert Langdon series. You’ll get interested and learn a lot about things that you did not bother to learn about before.

The authors have made the novel for the general public to realize the beauty of mathematics, in which they believed was best done through a novel because “... it is human beings who feel beauty and it is human beings who feel the immediacy of philosophical questions. And the only way to get human beings into the picture is to tell a story.” For what counts the most, they were successful.

A certain ambiguity

A Certain Ambiguity is a Mathematical Novel that covers the striking experiences of a boy named Ravi Kapoor. With His struggles and knowledge he gained in the field of Mathematics. It all started back when he was young, on his 12^th birthday wherein he was given a magical problem to try on the calculator given by his grandfather in which he enthusiastically solved. This part of the book suggests a loving relationship between a grandchild and grandfather linked through a Mathematical problem. As soon as he got the solution, he was immeasurably  happy and very excited to show it to his grandfather. Ravi could never imagine a better fate to the things his grandfather dreamt for him of being a Mathematician. Things changed as his grandfather died the night after his blissful moment with him. Without his grandfather’s guidance, Ravi became indifferent to Mathematics as he had said “without him, there was only the monotonous drone of doing what needed to be done”.

As years go by, through his father’s urgings he was accepted to Stanford and incline himself towards a career in economics and enrolled in a math class named “Thinking about infinity” wherein he met Nico Aliprantis their Mathematics professor in which Ravi thought was like his grandfather. In this class, they learned about many mathematical concepts and principles. Soon he found out of his grandfather’s past with mathematics still on hand with the articles that Ravi read. His grandfather’s comparison of mathematical methods to religion with it is the humanistic side of mathematics being portrayed and felt by mathematicians and Bauji was one of them.

This book covered a lot of many mathematical informations that many of them I do not understand. But by reading this book, the humanistic side of mathematics have emerged in place and was felt by mathematicians, but many like me never felt any of it. Mathematics as the title said is a certain ambiguity or a certain uncertainty for the views of mathematics vary from person to person. Some may think that there is a mathematical truth but others may also argue that it is only a product of human mind with no independent existence. This book relates axioms to existence of God and the opposing views of a believer of God and an unbeliever. With this book, the conclusion made by the author is believe what you believed. That is why I think this book is entitled Certain ambiguity for it leaves the readers of what they believe mathematics would be.

My favorite part of the book was during the discussion of Professor Nico, he was asked by a student that “If mathematics is beautiful why haven’t I ever heard anyone talk about it that way before?” Professor Nico answered that Mathematics is like a spectator sport, you have to do it to appreciate it, and doing it requires patience and perseverance. I agree with this statement. It is true that in order to appreciate mathematics, you have to solve problems, find solutions and find meanings of what you solve. But thinking of it is hard far more doing it, but with patience and perseverance one may know the true meanings of mathematics and will surely appreciate it.

Movie review: To Infinity and beyond

                Having watched all the episodes of the Story of Maths, I was able to see the evolution of math from just a tool used to quantify harvest and parcels of land into its application and relation with shapes then into the development of calculus  and lastly into the discovery of complex theory that seemed impossible to be understood and solved.

                The final episode of this installment focuses on the development of the modern mathematics brought about by a German mathematician named David Hilbert. Hilbert unearthed to the world a set of 23 seemingly unsolvable and significant problems in mathematics that still needs to find their solutions. By doing this Hilbert was actually initializing the birth of a whole new mathematics that the world has never seen. As mathematicians, many tried their best to give an explanation and try to provide solution to these 23 problems until almost all of these problems were answered over time. Mathematicians earned their fame from solving these problems like Cantor who first understood the concept of infinity which helped him develop his continuum hypothesis. Cantor was also able to influence other mathematician to develop theories, useful theories in fact, such as that of Poincare’s Chaos theory and the Poincare’s conjecture.

                During those times Hilbert was able to challenge the world because the problems he presented cannot be solved using the simple operations we’ve had back then. Instead to solve these problems one needs to grasp the abstract ideas and concepts underlying behind such problems as he believed that everything needed to solve these problems is already possessed by mathematics. But then everything changed when a man in the name of Kurt Godell gave a new perspective in Hilbert’s idea by saying that some of these statements cannot be proved creating a sense of uncertainty in the field of mathematics. Godell later formulated the Incompleteness Theory as an alternative means of providing a solution to a problem by stating that there are statements about mathematics that is true but proving it would be difficult or it cannot be proved but still it remains true.

                One part that I really appreciate in this episode is the part where Julia Robinson, the one who formulated the Robinson’s Hypothesis, tried to answer one of the problems presented by Hilbert but was unable to completely do so until Yuri Matiiyasevich completed her work. This is because it shows how persons of different race and origin would try to synchronize with people who they do not know for the sake and for their love of mathematics.  As the episode goes by many few names were mentioned who was able to contribute in the field of geometry, like Galois, topology, number theory etc.

                After watching the series I was able to relate how the development of mathematics reflects the development of the human society. By continuously improving mathematics we are finding solutions that we can use for a better tomorrow. I can’t help but think about the mathematics of tomorrow, what would it be? Is there something else that we do not know about? Is this all math has to offer? I honestly believe that there is still something out there a new perspective in mathematics that will define the future generation. I don’t know why I have this exciting feeling about the idea that there’s more to math than this and how I wish to be a part of it. This is what makes math alive the curiosity of mankind throughout history. Right now we might not be able to know what math will become in the future but I knew it would be something beyond what we are learning today.

Episode 3 story of maths

Frontiers of Space

     This episode discussed how spaces works in mathematics and how mathematicians discovered the mathematics that describes objects in motion.

     I am interested with first mathematician Marcus introduced, Piero Della Francesca. He is from the northern Italy, an artist and a mathematician. It helps me think that it is not only philosophers can be a mathematician but it can be anybody as long as he has the capacity to do and love math. Piero created an extraordinary output of his art. He represents three dimensional figures into two dimensional surfaces through the used of patterns.

     Marcus then traveled to France and found out more things about Renne Decartes. Decartes decided to become an army until he found some realizations on mathematics and philosophy and decided to leave his hometown and went to Holland. It was indeed a success to Decartes to have his famous ideas. He is the one who united Algebra and Geometry that leads to the creation of Cartesian Coordinate Plane. Another man from the school of Decartes, Marin Mersenne who published one of the works of an unknown amateur, Pierre de Fermat, who end up as a rival of Decartes as the greatest mathematicians in their times. I don't know this man but he works nicely in mathematics. He promotes solving mathematical problems through fun and games. I agree in his idea, it's an effective way to master mathematics. A little fun makes things easy.

     The next mathematician that was discussed was the famous Isaac Newton from Britain. This was my favorite part in the movie because I am one of Newton's fan. He was born in Grantland and was famous in his works in physics. He may not be totally recognized in works in mathematics but he had discovered my most difficult subject at present, the Calculus. He didn't published his works until he heard about his rival, Gottfried Leibniz. Leibniz had the same idea as Newton. He published his discoveries in Calculus and found a big trouble. If I am in that time I would stand for Newton. It was his right to claim his credit for his works. I felt bad for what had happened to Leibniz. He indeed given the credit for the publication of Calculus but then, he still been accused plagiarism.

     The next topic of the movie will talk about the life of Leonard Euler, who created number like e and i and the prince of mathematics, Carl Friedrich Gauss. Gauss at 24 years old invented the modular arithmetic but most of the people don't know him except in Gotingen, where he was known as a local Hero. At his early age, he had lots of discoveries including the pattern of the prime numbers. No wonder why he was known as the Prince of Mathematics and not as the Father of Mathematics, LOL. 

    All this men may have different personalities, origin, and ideas but still they were all the same. They were mathematicians who developed and opens the real world of mathematics..

A CERTAIN AMBIGUITY ~p

PAULA H. COMBISTA 

MST 3 MATH 1 

A CERTAIN AMBIGUITY 

Mathematical Novel, its a good approach to the readers to learn math and to enjoy reading it. Normally or most student find reading academic books are boring, just the thought of reading or just starting reading it make us feel dull and tired but reading fictional books like Percy Jackson or Hunger Games we feel trilled and excited we even spend money for it. So this mathematical novel really is a great idea, it easy to read and easy to understand and what I like the most is its in first-person (well I rather read first-person novels).

Another good thing about novel we could feel the feelings of the protagonist, the ideas he have, the experience he been through, how he will find himself and how he will succeed. Because knowing that sometimes we can relate and give us more ideas. Like in this novel we could feel his struggles, his love in math and all of that things.

Talking about mathematics, the book help us to see the beauty of math that if we just open our mind we could appreciate math. And remember those documentary film titled Story of Maths? About those Greek? Zeroes? Infinity? Theories? And those Mathematicians? Certainly this book is not just for entertainment but its a book of learning about the math, the human and the world. I remember a conversation between Nico and one of his student and I quote  “If mathematics is so beautiful, why haven’t I ever heard anyone talk about it that way before?”

“Maybe it’s because mathematics is not a

spectator sport. You have to do it to appreciate it, and doing it requires patience

and persistence. You can love a song without being able to sing, but

that doesn’t work in mathematics. Nevertheless, the beauty is there for you

to find.” And that’s how mathematics work-appreciate, patience, persistence and find the beauty of it. 

A Certain Ambiguity - Book Review

This was the first time that I have encountered a reading that says “a mathematical novel”. Math alone is hard and sometimes not that interesting, then you combine it with reading a very long story, which honestly, I am not very fond of. At the start of the story, a young boy and his grandfather go thru some mathematical problems and tricks with the aid of a calculator. Now as an occasional book reader, this really got boring, but as you progress in the novel, you can feel some sort of attachment to the young boy Ravi as he goes through his passion with mathematics the sudden heart-breaking death of his grandfather and many more events.

The authors’ approach in writing the novel is well thought out as he makes this mathematical novel can surely catch the attention and imagination of the readers. You can easily imagine the scenes that are happening as you read the novel. The ideas also presented in the novel are quite interesting as it shows how mathematics can be used to understand the world we live in. The way the novel was written allows it to show many view points and ideas in the field of mathematics and philosophy. One of the struggles or “questions” that can be observed is whether there can be certainty of truth in mathematics and in life. The continuous attention between life, religion and mathematics separates this novel from any other math books. It helps the reader experience a human and emotional side of mathematics and mathematicians.

The book is a good read. Compared to the previous two this was a very easy novel to read and understand. It gives much more life to mathematics and also mathematicians and a deeper understanding to the topics mentioned. 

The Story of Maths-Frontiers of Space Movie Review

The Story of Maths-Frontiers of Space

                As we continue this epic adventure thru the past of mathematics, we can now quite understand that most of what we have today, we owe to the development and advancement in the field of mathematics. The 3rd episode of the story of maths now takes us to Europe, and in the time where it has taken over the advancement of mathematics from the Middle East. We are introduced to René Descartes, one of the few mathematician-philosopher who realized that two of the major fields in mathematics today can be linked, algebra and geometry. We then venture into France, England and other places where mathematics has developed. Some developments were in calculus, the properties of prime numbers and more.

                Thru these advancement, we can now understand the world we live in a deeper perspective. We can see things in different dimensions and discover an ever changing world. It is very fascinating how philosophy, art and mathematics combined can change the course of history and the lives of mankind. Again we can conclude that without all the advancements in the past, we would not experience the technology and advancement we have today.

Movie Review: The Story of Maths-Frontiers of Space

“Without this golden age of mathematics from Descartes to Riemann, there will be no calculus, no quantum physics, and no relativity, none of the technology used today.”

            By now we have realized that mathematics has affected our daily activities in more ways than one. The first and second installment of the series of story of maths had explained how numbers have evolved to counting days, to finance, to creation of landmarks such as the pyramids. The third installment focuses more on the power of perspective-geometry.

            This series had named many mathematicians all over Europe, who, in their own ways developed and contributed ideas on geometry and calculus. Descartes, the prime mover of linking algebra and geometry had built the foundations in which other mathematicians like Newton, Liebniz, Bernoulli, Euler and many more have been known upon. Primarily, the third installment of the series somewhat summarizes the evolution of geometry and calculus in perspective with motion. As what Newton was famous for, his discovery of calculus helped us describe movement. Through this we were able to understand more of the complex changing world. Through the evolving discoveries from the foundations of Descartes which were passed on from one mathematician to another, it was riveting to have known from the ideas of geometry  and calculus, the shapes of space are being discovered. This discovery has allowed us to broaden our imagination in creating dimensions and perspectives we thought were non-existent at all.

Flagellation of Christ-Pierro dela Francesca
Source: http://en.wikipedia.org/wiki/File:Piero_-_The_Flagellation.jpg

            Like Pierro’s painting Flagellation of Christ, we see the play on perspectives brought to us by the ingenuity of the minds of our former mathematicians. It is interesting in a way that we can see that science and art are joined together to prove the existence of different shapes and forms of space. Because of the great contributions of these mathematicians in this field of science, we are able to be what we are, in our advanced technologies, in our present day.

            

Book Review: A Certain Ambiguity by Gauray Suri & Hartosh Singh Bal

“Maybe it’s because mathematics is not a spectator sport. You have to do it to appreciate it, and doing it requires patience and persistence. You can love a song without being able to sing, but that doesn’t work in mathematics. Nevertheless, the beauty is there for you to find.”

            Of the three math books I have read so far, A Certain Ambiguity has got to be the most interesting of all. I commend the authors’ approach in explaining the beauty of mathematics through what they call a mathematical novel. The book had its own way of captivating its readers-mathematicians and non-mathematicians alike, by involving certain ideas about mathematics, its philosophy and the beauty of the science concerning its surroundings. It was wise of them to incorporate the principles of mathematics in the life of a boy who grew indifferent to the science after the death of his grandfather.

            The book was written well enough to make its readers understand the beauty of mathematics through incorporating it in many philosophies in life. In this book it touches how mathematics can be a way of understanding the world-that it does not only focus on solving alien problems but it also has its way in contributing to life’s greatest questions. Mathematics, as explained in the book, deals on the certainty of truth. Philosophical, I know, but it does make a point for only in mathematics do we not consider a solution or answer, no matter how brilliant it may be, without proof. As quoted, “The historical acceptance of a statement as fact does not make it so.” Mathematics does not deal on how long an idea has been accepted, but the proof of the idea and its certainty.

            It is difficult to have to review a novel who holds more ideas than what is expected of a math book. It truly is a great and easy read. The book gives life to mathematics and mathematicians and how math has evolved and adopted to the present math community today. Out of everything, what truly is captivating about this book is it gives mathematics a human existence-that mathematics is not something alien but something human we can understand.

A Certain Ambiguity

3rd Book Review. A Certain Ambiguity

The first paragraph in the author’s note explains the whole meaning as to why this mathematical novel exists. It says, “Our principal purpose in writing A Certain Ambiguity is to show the reader that mathematics is beautiful. Furthermore, we seek to show that mathematics has profound things to say about what it means for humans to truly know something. We believe that both these objectives are best achieved in the medium of a novel. After all it is human beings who feel beauty and it is human beings who feel the immediacy of philosophical questions. And the only way to get human beings into the picture is to tell a story.” While I read this, I thought, “Who would write a novel with mathematics as a major supporting tool? This would be weird and this won’t work.” but I was wrong. This mathematical novel was a great reading material. It explained all mathematical aspect in the novel well and it was easy to comprehend. Even people who are not mathematically literate would understand this since every concept is well explained and introductions for each concept are given.

The positive thing about this book, as said above, is that introduction about a concept is given so it is easier to comprehend. An example for this would be about the prime numbers. The students were arguing if someone was certain about something and prime numbers were brought up. (This was stated when they were at a party. It still fascinates me how they could talk about “nerdy” stuff in a party.) The authors did not have to explain the meaning of prime numbers but they still added it. I think it is a good addition for those who are mathematically illiterate.

The writing style of the novel was a bit different for me but it is understandable since the authors of this book are mathematicians and not professional writers or novelists. I think proper grammar and writing is not needed when explaining scientific or mathematical stuff as long as the main idea is presented and understandable. The characters for this novel are also interesting. While reading the book, I thought that the characters where really smart and intellectual. Who would talk about their lessons in a party?  Usually, you would want to forget about everything that’s giving you stress in a party but these students were different. They made the novel entertaining.

The characters are fictional but there is one character I want to meet if this was real and that is Nico. He makes everything about math look appealing, beautiful and everything positive that not all could see. I was also once fascinated by math but drifted away from it. I wish to meet a person like him for me to see mathematics again in another positive light.

All in all, this book was a good read. It explains to you mathematics in a different way. The authors were successful in explaining mathematics in a novel though it was not well written. I am also not sure about them showing that mathematics is beautiful. It depends on the person reading if they saw mathematics as beautiful after reading this book but I saw this book as inspiring, interesting and fun.