A Bird’s Eye-View on Algebra: A Written Report

I’m glad I was assigned to be on this group. Among all the topics offered, Algebra appealed to me the most. That’s because I’m not a fan of Computers and its history, much more Statistics (I’ve had a bad experience with this one).. I also had no idea before about most of the Number Systems, and I don’t think I have that much interest about Geometry. By the way, our group has seven members; two smoking hot males and five drop-dead gorgeous females, and I think we get along really well.

In the presentation of our topic, we’ve planned two games, a video presentation, and organized an informal debate.

Let me start with the two games we’ve planned to let our classmates participate. First was the famous amazing race, which was composed of six stations and one pit stop. Of course, the Algebra air was very evident in every station as we really prepared games, puzzles, and problems to keep it challenging and fun. They had to complete the stations before going to the pit stop. I think my classmates appreciated our effort and they were entertained. The second game was a derivative of the game ‘pass the message.’ Haha. The goal was to pass on the number problem to each member of the group in a straight line to be solved by the last person. It was both crazy and fun, every group was very competitive. While we were watching in front, we just can’t help but smile and laugh because our classmates were having a good time.... maybe.

Let us move on to our debate. A week before our actual presentation, we had a different idea in mind about the topic which we were going to focus on the debate; it was the question ‘Is learning Algebra really necessary for Biology majors?’ we were interested about. But when we consulted with Ma’am Cielo, turns out, our idea wasn’t quite appealing and enough to actually argue about on the debate. Well, she had a point. That was quite obvious. There’s no need to take that to the floor to know the answer. So Ma’am gave us an idea. We actually did not think of that one until she mentioned it. So thanks to Ma’am Cielo, we were able to find an interesting subject to debate about. The problem states; ‘Which Mathematical perspective of Algebra should be prioritized on secondary and tertiary levels of education?’ At first, I really, really thought that the government side would win... as it often does. Haha, I was left in awe after the audience’s verdict showed that the opposition side won. What the government side supported was to teach Algebra in an operational perspective focusing on operations, equations, formulas and inequalities, while the opposition side believed that it should be the conceptual approach that should be prioritized which focuses on explaining the different concepts behind Algebra. In my opinion, I think we need both. I don’t agree that one should be given more priority than the other. Anyway, our debate went well more than expected. We were just so nervous before we started as every one of us was not that really prepared. My job wasn’t that important but I’m just so glad my group-mates pulled it off really, really well! I was amazed that both teams really presented a good argument. I’m relieved now that I was able to do what I had to do even though it wasn’t as major as those that were done by the rest of our group. This was an experience that really has taught us a lot.

Our group presentation revolved around the topic of ‘Consumer Mathematics.’ We merged two Pinoy mainstream shows Matanglawin and Mutya ng Masa to create a video presentation. We assigned two of our group-mates Zam and Nykka, to act as Kuya Kim and Doris Bigornia. This was the first concept we had in mind and it was the one we really tried to make possible. Due to our stress-filled weeks prior to our presentation, we did not have the luxury of time to bonggaciously prepare for it, so we settled for a week’s preparation. We’re glad it still went fine. The real flow of our story went like this; our classmate, Kuya Zeul, was the one who acted that he wanted to start a soap business but his money was short, so he had to loan from a bank in order to complete the required money for the business. That’s pretty much the gist of the story and that’s also where Algebra came in. Doris was the one who came up with the idea to loan from the Official Pautangan ng Bayan bank, where I was the banker, while Kuya Kim on the other hand, was the one who helped in finding the perfect formula for a good and marketable soap, with the help of a Scientist played by Jaina. An advertisement of the soap featured Sharmaine as a stunning girl using the product. Then, an interviewer, played by Marielle, asked the public’s response to the Kalapati whitening soap. When the soap was properly received by the public, Kuya Zeul gained back what he loaned from the bank plus his profit. When he paid the money he owed plus the interest, it concluded the story. Both Doris and Kuya Kim helped Kuya Zeul achieve his goal. I know we could’ve done better if we only had a lot of time; there would’ve been more sound effects, more scenes, and more funny details. But even if our video was only short and was still kind of raw, my classmates really thought it was fun and good and that’s just what we needed after all the things and efforts we have done for that video. The whole process of planning and making it was honestly, something to remember.

We were able to get a bird’s eye-view on Algebra because of this report. I’m proud to say that we have done all these and that even though it was not perfect and extravagant, it still made all of us laugh and learn something. I’m just glad we’re already finished. From the first group, the Number Systems, to ours, the Algebra, I just keep finding myself learning Math in a different and fun way. I wish it was like this all the time when I was in grade school. Hehe. Furthermore, there were two important things I have learned from this experience; first, Algebra, no matter what perspective you’re looking from, it is very important in honing your arithmetic and thinking skills, and second, that in every group, cliché as it may sound, teamwork is really, very important (that should be emphasized), because once even just one member of a group fails to contribute on all the works needed to be done, there will surely be things that can go wrong in the whole output. Well, I think that’s all there is to tell. Over-all, I have to say that it was really a fun-filled learning experience. Looking forward to the upcoming games and group presentations! J

The Unveiling of Algebra: A Written Report

            We have been in a constant battle with algebra. We have been in several situations where we are faced with these mathematical statements with letters and numbers combined and associated. Some of us hated being those situations. However, nothing beats the feeling of being able to solve these mathematical statements and arrive with the right answer. That is such one glorious moment!

            This is one of the reasons why we chose algebra. I believe that each one of us in that Math 1 class has his/her fair share of memories with algebra. We want to be a part of something that will relive those memories again. Though some of them are bad memories such as failing an exam in Math 11 or Math 14, they are still memories that left us with lessons.

            Moreover, algebra has been tied up to all the important aspects of our society nowadays such as in education, in technology, in economics, in politics, in health management, in research, in statistics, in practically everything. It has laid out a strong foundation of knowledge from where a lot of technological advances have been developed from. I cannot imagine being in this superbly technologically advanced world without that theorems and equations established by mathematicians from the concepts of algebra.

            Being a part of Group 2, the Algebra group, I was able to learn a lot in the short adventure that we had in learning the deeper concepts of Algebra. For us to be able to share concepts of Algebra to the whole class, we need to first learn it in a deeper level. I believe that as a group, we had a good grasp of it.

            We were tasked by Ma’am Cielo to have a debate related to issues concerning algebra, a creative presentation that would highlight the applications of algebra, and games that would challenge the capacity of our fellow classmates in the field of algebra. As a group, we have decided to follow the time table shown below:

Date	Activity
February 5, 2014 (Wednesday)	·         Amazing Race
February 7, 2014 (Friday)	·         Debate(Operational vs. Conceptual) ·         Video presentation (Muchacha ng Masa) ·         Games (Pass the equation)

February 5, 2014

            Since an amount of time was taken from our assigned date because of the unfinished presentation of inventions by each group, we decided to move the most important parts of our presentation such as the debate and video presentation on February 7. Instead, we had the amazing race. Ma’am Cielo briefed us about the possible strategy that we could use for the assigned subtopics. She advised us to incorporate the subtopics such as relations and functions, linear function and its graph, and solutions to linear equations to our games.

            There were five stations to which each member of our group has been assigned to. We decided to balance out the tension in choosing the games that we will use. There are those that are so mind-boggling and there are those that will serve as a breath of fresh air. For example, in my station, I asked them 4 questions and will be given 1 minute to answer each. The twist of the game is to spell the correct answer through “butt spelling”. They were so fun to look at in my station.

            I believe that the groups had fun in each of the station despite how difficult it is. They were able to exercise their teamwork. Despite being covered up in sweat through running in different stations, I witnessed smiles and laughter.

            At the end of the game, this ranking of the groups was achieved:

Computers – 1^st

Number Systems – 2^nd

Geometry – 3^rd

Statistics – 4^th

February 7, 2014

            We decided to start the day with the debate. The debate revolved on the notion “Which mathematical perspective should be prioritized in secondary to college level education: the operational approach or the conceptual approach? ”. We decided to use this notion because I think that this will be a tough debate. I myself know that those two approaches are very important in teaching algebra as they are essential in understanding the whole idea of algebra. I felt that it will be a great challenge to us to convince the audience that our side is better.

            Before the debate was officially started, the votes of the audience were obtained. 8 votes went to the conceptual team. On the other hand, 7 votes went to the operational team. I thought to myself, “This will be a very close fight. This is going to be tough.”.

            The arguments of the operational team revolved on the fact that algebra is built based on operational thinking. They stated that the operational approach is more efficient and more practical. It is specific yet universal. It may be dependent yet straight-forward.

            The opposition team, the conceptual team, focused on 4 arguments. First, math is inherently conceptual. Second, the conceptual approach builds a foundation of knowledge. Third, the conceptual approach is general and can encompass broader fields. Lastly, the conceptual approach removes dependency on ready-made solutions.

            I noticed that the audience was actually giving responsive reactions to most of our statements. They were connecting with us. It is hard to establish such connection because some people find debates boring. To be able to establish such connection, I think that is the most important thing that we have achieved. Moreover, when we obtained the votes at the end of the debate, the score was 13-1, in favor of the conceptual group. This showed that one team was able to state strong points that have encouraged the audience to switch their votes.

            We decided to ease the tension by having our short video presentation. Ma’am suggested that we apply consumerism mathematics in this part of our presentation. We chose a plot wherein a student (Zeul) does not have enough money for his enrolment so he asked for help from Doris Bigornia (Nykka) who later seeked for help from her friend, Kuya Kim (Zam). They figured out that they could loan money from the bank with an interest per annum of 3.5% and have a soap-making business. The soap-making business turned out to be a success. The student was able to pay his loan with interest and was able to obtain money at the end for his enrolment. We incorporated the concepts of interest, gross income, and budgeting in our presentation which are also involved in the algebraic concepts.

            The plot may not be complicated. However, I think that what made our presentation unique is that it has humor which can be seen in the lines used, the characters being played on, and the delivery of each scene. The whole class was actually laughing their hearts out throughout the presentation every time a new character was exposed. I, myself, was laughing all throughout.

            There was still some remaining time left so we decided to play a game. It is derived from the game “Pass the Message”. Instead, equations were passed on and the last person needs to solve for the x in each equation. We started off with a difficult equation and noticed that the class was not that hyped up. Then, we decided to give simple equations that will challenge their swiftness in solving. It was when the groups started to really battle it out. The results of the game can be seen below:

Geometry - 3 pts.

Number Systems -2 pts.

Computers - 1pt.

Statistics - 0pt.

            Encountering mathematical statements with letters and numbers associated with each other may have been a fear to some of us. However, with the right perspective in teaching and learning them, we will be able to see that there is beauty in these algebraic equations, formulas, and theorems. Fear will be eliminated. We will all be able to love algebra and to love the totality of mathematics, as well. J

For the first time in forever

            As I read the title of this book, my mind was boggled by the paradoxical statement. A certain ambiguity indeed encapsulates how I have interpreted it and how I felt after reading it. However, one thing is for sure, I didn’t really enjoy it much and I was quite bored and distracted due to the overloaded information that this book brought about. This book review will not be a very good one because I was distracted while writing this for I was not really into reading the book but still, it was quite enjoyable and I really do not know how I feel after reading that. So here it goes anyway..

            It opened up with our main character, Ravi Kapoor, as he reminisces his childhood and in it, he remembered how his mathematician grandfather influenced him in liking mathematics like teaching him mathematical tricks and giving him a calculator on his 12^th birthday. But the interest gradually faded after his grandfather’s death. The loss of his grandfather was definitely a great factor of him being unresponsive towards mathematics. The next highlight was when our main character studied in Stanford University but wasn’t really sure of what he wanted exactly. Then he met a professor whose name was Dr. Nico Aliprantis who summoned him and his friend Peter, to take his class which was “Thinking about Infinity” and they agreed. This professor of his knew his grandfather because of one of his papers. In this same class, our main character also meets the love of his life which was Claire whom he marries eventually. She was a gardener who had a particular interest in mathematics. In this class, the main focus of the mathematical topics was strongly pointed towards the idea of infinity. In here, they learned the concepts like Zeno’s paradox, Cantor’s theory of transfinite cardinals, Zermelo-Fraenkel axioms of set theory, the independence of the continuum hypothesis, etc.

            Then, Ravi discovers that his grandfather was detained because he was accused of blasphemy because he does not believe in the existence of God and he supported his claim through the use of nothing more than mathematical knowledge. It was a very sad realization that people were not able to speak their minds freely in those times because freedom of speech and expression were not really accepted by the society. The conversations of Ravi’s grandfather and the judge were also very fascinating. In the said conversations, they have discussed about Euclidean theorems which tried to define the conviction and inevitability of mathematics. There was also the mathematical axiomatic method discussion between the two.

Despite the fact that this book was jampacked with mathematical ideas, topics etc., which kind of made me stare on to my screen, I still liked how elaborative the authors have been in this book (If only I were that interested in mathematics, maybe I’d appreciate it better). But there was one statement that really disturbed me and that was “Christians are people who gave up on reason.” I actually beg to disagree because as I have seen and read in some references, philosophers and scientists have been using mathematics, science, philosophy and the likes in order to prove God’s existence. So there goes all the reasoning that is needed.  I would like to elaborate more on that bit but I’d rather not ‘cause I don’t want to go all philosophical here and this is a mere book review so I’ll stick to the reacting part but yeah you get my point.

There is really nothing more to say and I still haven’t reached 900 words so I’ll just keep on blabbering. But I did learn stuff which I’m not really sure how I could apply into real life situations. Stuff like the lessons that they discussed in Dr. Aliprantis’ classes were dumbfounding (just because I don’t understand them) but they were interesting all the same and if I would have some free time, I might read some more about those (maybe, I doubt about that free time though). Maybe in the future, I’d look back and remember this novel and read it again. This book has definitely given much information for its readers to internalize but it would really depend on the reader. This book would really be recommended for those who are mathematically inclined (and not those who major in Biology lol). I guess the title refers on how philosophical mathematics really is and I guess some things should be left uncertain because in that uncertainty, the limit does not exist.  

           

            

A Book Review: A Certain Ambiguity

A Book Review: A Certain Ambiguity

                A Certain Ambiguity is a mathematical novel. You read it right. it is a mathematical novel. It was not just an ordinary novel. The story has an amazing and sophisticated plot, characteristics that for me only pure authors could give. I am pretty sure the authors, Gaurav Suri and Hartosh Singh Bal are mathematicians but I am very impressed with their book because they were able to match literature and mathematics in an unexpected and unique way. Honestly, it was my first time seeing and reading a mathematical novel. Before reading it, I thought that it would just be about another run down of Mathematics history and how the early and modern mathematicians were like, what were their struggles and stuff like those. Surprisingly, it was a complete turnover.

                The story started when a 37 years old Ravi Kapoor reminisces precious moments with his Bauji. He was remembering how his grandfather has stirred his interest in math when he gifted him with a calculator on his 12h birthday and how he loved being up with his challenges. Then that interest just started to fade when his grandfather died. Though he still excels in school he never found meaning in doing so. He never found beauty in all his subjects especially mathematics which he used to like. Following his grandfather’s will, he went to America and studied. He went to Standford University but he was like a body without a soul. Yes, he exists but same in high school nothing stirs up his interest. He could not even choose a major if not because of his father.

                One time, he and his best friend, Peter Cage, stayed late for a gig and there he was able to meet a mathematics teacher named Nico Aliprantis. Nico invited them to enrol in his class “Thinking about Infinity”. Not knowing what has urged him, he signed for that class. In their class different students enrolled. Each one has his or her own way of thinking that added to the excitement of the course. Then one time, Dr. Aliprantis had told him he happen to know his grandfather through one of his papers. Of course, Ravi wanted to know this part of the story.

Going back to mathematics, the mathematical concepts and ideas of Zeno and his paradoxes was the first to be mentioned in the very first meeting of the class. There was also the Incomplete Theory of Godel and Paul Cohen’s Consistency Theorem. There was also a discussion about Euclid’s axiom and the non-Eucledian geometry. It was also mentioned that during the time when his grandfather was in America, that was also the time when Albert Einstein’s General Relativity was confirmed. At the end, Ravi got his interest back in mathematics and eventually acquiring a career in it through economics. As for his love of his life, he married Claire. Remember one of his girl classmates whom he sat beside on the day that he found about his grandfather’s imprisonment in America?!

As for the book, I may have said it earlier but it was really amazing. It was amazing how they have come up with a story that even those unappreciative of math can appreciate. Well, the authors have said it at the author’s note that they want people to see the beauty of mathematics and to let people realize the importance of mathematics. And they think that telling a story is the best way because it is what human beings like. They have also incorporated equations and illustrations for the readers so that it would not leave them imagining what were going on just by reading the text. Even though it is a mathematics novel, they were very meticulous on details that they did not confine the story just on mathematics or Ravi’s life. They did not forget to add spices to the story, say, Peter Cage’s religiousness and the fondness of some characters on music. Philosophy was also taken into account. They made it in such a way that every character has a story to tell.

Generally, it was a refreshing way to learn and appreciate math. It is a novel that is child-friendly because it is an inspiring story of how a child began his love for mathematics and how he was able to cope with his loss and eventually finding himself loving again what he used to love, MATHEMATICS.

Not Just An Ordinary Novel

            I don’t like novels, but this.

It has been a great challenge for me to read this book and eventually make a review on it. I haven’t read novels, I don’t read novels, I just don’t want to. Apparently, it became a requirement and more amazingly the first novel I have finished is not just a mere piece but a mathematical one. I would admit that at first I was hesitant to read the book since I have no idea if it’s a creative work or very technical. I even expect this book review to be the worst one I’ll ever make since I have no idea how to criticize a novel. Well, here’s a try.

            Before reading the story, I tried skimming my high school literature notebooks to refresh myself with the characteristics of a good novel. I felt a natural drive while reading through the storyline. The twist was that math was the natural drive. It has given me great amazement how the authors sewed concepts and theories of mathematics in each chapter of the novel. They were also successful in making a mathematical novel that can be understood by those who aren’t really into mathematics and I believe their primary goals were efficiently achieved.

            Generally, the novel was about the mathematical journey of Ravi Kapoor from his childhood to taking into a mathematical course. There he learned the interconnections and relationships of mathematics to the universe. Many obstacles have then bewildered the main character as he went through answering some questions while applying concepts he had learned in the university. There were also many twists in the plot, but the ‘love’ part has not bothered me anyway.

  It was of great surprise that philosophy has again entered into the plot. I didn’t see it coming since at first, the novel started with a cute kid trying to figure out how magic in calculators works. It all started when Ravi took a course in Stanford. However, when he was about to enter college, his mother was a bit worried due to financial difficulties but good thing Bauji had prepared enough to finance his education. In the university, he met Peter whom he eventually became friends with. All the twist started when he got into a class which was quite interesting. The course was “Thinking about Infinity” under a bright professor named Dr. Nico Aliprantis. It was also in this class where Ravi met Claire, which eventually became the love of his life. There, they started to learn Zeno’s paradox. Also, they discussed various theorems that tackle infinity just like that of Galileo that “one cannot apply the laws to finite mathematics to infinite sets.” Also the Cantor’s theory of transfinite cardinals, Euclidian geometry and many others were also discussed. With immense astonishment, I only thought that the story was just technical, however, it seemed perfect how the theorems they learned can be used to study religion and philosophies and other abstracts that exist.

            Ravi has then tried to unravel and investigate the imprisonment of his grandfather. He had read through the newspaper the issues of the statement of his grandfather regarding the inexistence of God using his beliefs and knowledge in mathematical concepts on infinity. Thus, it was considered blasphemy in his small town where almost all people believed in Christ. Well, this part grew my eyes bigger. How could a mathematical concept or statement be used to conclude that a supreme being does not exist? Maybe I would believe that some scientific or historical basis can do, but why math? I then remembered the first book we had when philosophy was related with math. Going outside the realms of the story, it quite bothered me how it was really unacceptable in those days to speak out what people truly believed in. I remembered taking a course in “Panitikang Pilipino” that the author should not directly state the era of the story but rather show some instances. In this case, one can conclude that it occurred a long time ago. It is somehow overwhelming to see how the society accepts rational and radical people in today’s generation. Furthermore, if his grandfather had committed that in the 20^th century, then he should not have been arrested for blasphemy.

            I felt the technicality of the novel reading through the personality of Judge Taylor. The “creation axiom” of the judge was indeed something to be amused on. I would really like to recognize how the authors perfectly used math to some explanations in faith and rationality of mankind. As a Christian believer, I stand by my faith that indeed the whole concept of a supreme being could not be explained by mankind. Then I realized that human intelligence had really been trying to pursue and generate theorems that can establish an answer to questions regarding religion and faith.

            The novel was indeed ambiguous. It vaguely covered each part of the story; however, it has distinctly discussed mathematics and philosophy in a strategic way. The way the authors put in the concepts of mathematics in the whole story was unbelievable in a mode that an ordinary student in the university could precisely understand it. Furthermore, I am really not quite sure about these comments and critiques I have made on the novel since this was really the first time I have read one. A lot of other novels would be great to read but this one is unique. It was informative, technical, and creative. However, I will still not read novels unless it’s a requirement.

Say What Now? By Edwin Banquerigo Jr.

A book review on A Certain Ambiguity A Mathemitical Novel by G. Suri and H. Singh Bal

“Say What Now” was the first three words that I used when I heard that we are going to make a book review about a mathematical novel. I like Sci-fi movies or anything that involves science and a great story plot but I was not really expecting to see and do a book review about a math novel.

Mathematics was involved in every part of the book. Principles, theorems and mathematicians are intently woven in the storyline which I give the authors an explicit high five for a job well done. Tsing Clap High Five. This book also involved serious philosophical aims which would contradict point of views of the believers; you do not want them as bashers.

Ravi Kapoor the main character in this book is fascinated by philosophy and mathematics but before we elaborate that further let me show you how Ravi discovered mathematics in his life. Ravi’s Grandfather gave him a present a calculator and a math problem on his birthday; by the way the grandpapa of Ravi is a great mathematician so for me this is like the cliché version of the mathematician handing down their great legacy or a heirloom for instance to the younger breed of their kind. For me if I was Ravi I will not accept the calculator but instead ask for a toy car or a ball for instance but Ravi was happy with the gifts and this opened his mind to explore mathematics even more.

Another cliché that is commonly found in novels are a death of a special someone or the most influential person in the life of the main character. In this book Ravi’s grandfather died, but lucky for Ravi his grandfather left him some funds to pursue his career in Stanford University inclined to Economics. Mathematics is pretty much involved with Economics, so yeah that explains a lot. So he goes to Stanford fueled by hopes and dreams, his mother constantly reminds him to do good in school in order to have a great job and help his family with the financial difficulties. The slumdog in America where he gets to fulfill his dream, you know where I am getting to. Moving on..

Ravi met Professor Nico who also specializes in the field of Ravi’s Grandfather. What a great coincidence. He took the course “Thinking about Infinity” where Professor Nico was teaching. Ravi and Prof. Nico had this little chat and then he mentioned his grandfather and then suddenly the Professor knows his grandfather and suddenly looks for the book his grandfather wrote and found a footnote stating that his grandfather wrote this book while he was imprisoned.

This was the shocking revelation that pumped up every antagonist in most novels. Finds one plausible secret and suddenly gets pumped up in search for the truth and know the reasons behind. Funny point is that the grandfather of Ravi was imprisoned because his mathematical ideas were considered as blasphemous? Who the hell imprisons a smart ass guy which is not a threat to the national security basing it only to his ideas? I mean ideas do not kill people unless your idea is to kill people and he is just human so he can basically have his ideas and it depends to the people around him if they will believe in him. Then Ravi started exploring how his grandfather got imprisoned and started to question and did some research that would help him know the truth. Typical things that any protagonist would do in any movie or story; he learned so many things that enlightened him changed his views and all.

One thing that I do not like about this book is when they were not able to respect and recognize the people that have faith in God. Unlike the first mathematical book that I did a book review, this book did not give a damn about faith. The book represented by the author considers faith as irrational and lacks reasoning. Mathematics is based on facts and obviously mathematics should not rely on things that are not present by the time being or things that basically you put your faith on. That does not apply to my Faith in God. People tend to believe in something that would help them realize and rationalize things that are unexplained for the time being. Our human capacity is just so minimal we can not explain everything that is why science and all sorts of field married to science can not explain everything. Just like the Story of Maths Part 4 even mathematics can not prove everything. Mathematics helps us a lot and really has a lot of reasoning behind but for me I believe in God but I still have a lot of reasoning behind my brain. Scientists, mathematicians and physicists or whatever icist or icians you are; one can never show or prove how man came up to this earth and explain the wonders of nature. That is just how life works, and if you are really reasonable enough you will start believing in God.

I got a little carried away with the argument on the book about math and religion sorry for that. The book presents mathematical theories, postulates and many things about mathematics and its builders. Some people mentioned ring a bell like Paul Cohen, Euclid etc and so many other people. The story plot was a common one and has a typical happy ending because Ravi turned out to have a happy life and basically it is just a happy ending. Do not worry because the math part and the arguments will totally stir up your mind juices and will totally get rid of the boredom. Good Read and it is definitely better than the first book that we did a book review on and basically you are going to say Say What Now while reading the book. Adios

The Story of Maths 4: To Infinity and beyond

Now, we are on to the last episode of the BBC documentary, Story of Maths. The documentary has shown, from the very first episode down to its last one, the history of Maths, how it evolved, developed and flourished through time.

The final episode considers the unsolved mathematical problems that were faced by the great minds of the 20^th century. As mentioned, “Mathematics is about solving problems and it’s the great unsolved problems that make Maths really alive”.

In the International Congress of Mathematicians, David Hilbert, a young German Mathematician, boldly set out what he believed were the 23 most important problems for mathematicians to crack. These problems redefined the Mathematics of Modern Age.

It was George Cantor who proposed who really understood infinity. It was suggested that the infinity of fractions is much bigger than the infinity of whole numbers but later on proved that the infinities of both whole numbers and fractions have the same size. There was one problem that Cantor could not get over with for the rest of his life, the Continuum Hypothesis.

Fortunately, there was one mathematician from France who stood up for Cantor and believed that Cantor’s new mathematics of infinity was beautiful. He was considered to be the greatest mathematician France ever produced, Poincaré. Paris became the center of Mathematics and it was Poincaré who shed light to the world of Maths during this time.

In 1885, a prize was given to anyone who could establish mathematically whether the orbit would continue turning like clockwork. Poincare simplified the problem by making successive approximations to the orbit which he believes would not affect the final outcome significantly. His ideas were sophisticated enough to win him he prize. However a problem was identified and that Poincare made a mistake. His simplification didn’t work because even the small change in the conditions could affect the results. The orbits Poincaré indirectly led to what is known as the Chaos Theory.

An 18th century puzzle was presented: “Is there a route in the city which crosses each of the seven bridges only once?” It was Leonard Euler who solved the problem. He realized that we don’t really care about the distance because what really matters is how the bridges are connected together. This is the problem of the new set of geometry, the position: the problem of topology.

Topology evolved as a powerful new way of looking at shape because of Poincare. Some people refer to topology as bendy geometry.

In this last installment of the documentary, I seriously thought of how I could connect Mathematics into my course which is Communication Arts. I admit, I still wonder whether there is significance between math and communications or not. However, on second thought, Mathematics after all is communication in itself. It contains a technical language, spoken not only by a few great minds, but even us, ordinary people. And that both Math and Communications have theories as foundations of their study which of course, should be and would be put into practice.