The Allegory of the Clever

There are a whole lot of things the subject mathematics can cover. As I have highlighted a few articles ago, Mathematics is the language of the universe or almost everything. Anything that studies the relationships and interactions between variables, quantities, and change is mathematics. It is a very abstract concept.  Mathematics is the expression of the logical concepts and forms more complex concepts out of these basic logic. It is a logical progression.

Out of the book I had read an interesting fact. The logic of something ‘advanced’ is clearly complicated. Intermediate facts are usually simple. However the simple or the elementary facts is actually more complicated than the advanced. It may be the reason why we say that mathematics is a very difficult subject.

                Our notion of mathematics is basically a series of unending computations and all the other boring stuff in blackboard. Every math thing being taught in school is always about the principles, the theories, the calculations, and the algebra.  Mathematics taught in school is always our perspective of mathematics. However, Professor Ian Stewart in his book ‘Cabinet of Mathematical Curiosities’ had led my math path to a different, odd way. It is absurd and intriguing as he uses mathematics in games, puzzles, stories, and facts. There I found the fun on using logic, statistics and geometry in situations I have never thought of. I had compiled all my favorites from the book and these are some:

                Extracting the cherry. Well, I think everybody already knows how it is done. It is having the cherry out of the glass figure and the thing you will do is to move two matchsticks. I sometimes play that game when were eating out just to check if I have remembered how it is done.

                Much Undo About Knotting. Knotting, for me, is a Boy Scout thing. The facts raised by Ian Stewart drag my interest in knots. A mathematician’s knot is a different kind of knot having two ends stick together. It was that simple until I found out that the Knot theory is used in the study of molecular biology. It is already used in the mysteries of the DNA and in quantum physics.

                Perpetual Calendar.  It was more like “Great idea. I’m gonna use this on my desk tonight”. I had not really solved the problem.

                Mathematical Jokes 1. It has been hard for me to understand the joke. I was looking for something in that joke to laugh about but then I saw the warning. So, I skipped.

                Why Does Minus Times Minus Make Plus? It is arithmetic. We have already mastered this in school.  The highlighted problem there is how it is applied. He explained the problems in banking and debts.

“Well, if the bank kindly writes off (takes away) two debts of £3 each, I am £6 better off – my account has changed exactly as it would if I had deposited £þ6. So in banking terms, we want (-2)x(-3) to equal +6.”

I may have not thought of that. If we are to apply and use that, we will be confusing ourselves and also complicating arithmetic. The fact is somehow clever and I realized that simple math is more complex than advanced math. Just saying.

      The Bridges of Konigsberg. Ah, the Bridges of Konigsberg. It is somehow famous for having no existing solutions. This simple puzzle works as having to cross one bridge only once. I have also tried the puzzle several times and I had an existing proof that it very impossible. However, Euler, a mathematician, made a point that the geometry is not relevant in this situation. What matters is how everything is connected. Somehow I had made a philosophy that you cannot always have to entertain all people even if it is hard for you to prove your worth. It is very important to just maintain a good connection to these people.

Magic square. It is also famous ancient mathematical problem and a coincidence. The magic square is astonishing in a way that each row and column equal to 15. The ancient Chinese really knows how to play with numbers.

All of these games and concepts are clever. Ian Stewart has brought my mathematical perspective to a different world. Aside from the puzzles, He also had highlighted the concepts and the history of pi, Fibonacci and the golden numbers, Fermat’s theory, Pythagoras and the triangles, Euler’s principles and a lot more. It is a really good read and people might have enjoyed math out of it.  

A book review on Cabinet of Mathematical Curiosities

                Math in both elementary and high school was a little bit challenging, fun and somehow easy. When I entered college I thought it will all still be the same, what I thought was wrong. Mathematics in college was ten times more challenging, boring and was never will be easy. So I wondered how do mathematicians look at math that exciting and fun? In the book of Professor Ian Stewart; "Cabinet of Mathematical Curiosities" he discussed where the real fun is. Through the years Professor Stewart has been filling his cabinet with mathematical games, puzzles, stories, and facts. Written in his book are the different answers to different questions that each person might have about how mathematics work. The author had discussed different logic behind games, puzzles by using the science of mathematics in a fun and entertaining way.

                The author created an atmosphere where he as the author can interact with his readers through asking them to solve and perform puzzles and problems. I like the connection he makes with his readers however, since I am not a fan of mathematics I eventually got tired solving his problems and instead I skipped some of it. The book was not arranged in a chronological order, each chapter is not directly connected from the previous one which makes it less boring because each chapter opens a new topic.

                In the book my most favorite part was on the chapter of Curious Calculations. During elementary and high school I find it fun calculating lengthy mathematical problems but when Professor Stewart showed an easy and even more fun way to solve problems I realized how different mathematical problems in college could also be solved that way. It's like solving puzzles and the answer itself is the prize.

                His book was indeed a cabinet of mathematical curiosity. I myself was not that curious about mathematics but when I read his book I realized that my mind has a cabinet of curiosity that was yet to be filled with answers.

A written report

                All groups were assigned to create a debate, game and movie about the topic assigned to us. Our group, being the last one to perform and entertain our classmates was assigned to discuss about the broad world of computers. I thought it would be easy to discuss about computers since we are currently living in a computer generation, where there would be various topics to choose from to suffice the necessary topics needed for our debate, game and movie. However, I never thought of the idea that our group was assigned during the hell month of the semester. I even thought that we would not perform anymore since we have no time left. Unfortunately or let's just say it was a blessing in disguise that we were still able to perform, entertain and add some information about the world of computers.

                First we started with our game. Just like every group we decided to have the theme of amazing race however, due to the bad weather we played inside two different classrooms. It could be more fun if the game was outdoor, to avenge from all of the running that the other group had done and to feel the spirit of the race. Our second event was our debate; the stand was "This house believes that illegal "downloaders" should be punished". In the government side was Omid Siamard, Kissel Cablayda and Klimpol Maganaka. Under the opposition side was Ruth Nasibog, Claire Jacinto and Me, Ivy Gail Doringuez. The point of the opposition side was basically about having an easier access to different entertainment material at the most convenient and safer way. It would also be very impossible to put into bars all the people who are illegally downloading. Majority of the class voted for the opposition side since almost all of them are illegal downloaders and the practicality of downloading illegally.

                Lastly we had our movie with no title at all. The movie was basically about a teacher who got killed by a mysterious killer. On the crime scene there were bloods seen all over her body however, there were no lacerations. Her students, Gregory (Edwin) and Omid decided to test the blood using the Blast Software, only finding out that the blood contains the DNA of a cat. I was the killer in the movie being a cat lover and a person who loves her job who envied the other teacher (Klimpol) because she got the promotion I thought I should rightfully have.

                It amazing how math had evolved through time from simple numbers to gigantic computers. The innovations around the world are mostly because of computers. Indeed computers makes our life easier, it open doors to new discoveries and learning.  

Curiouser and Curiouser

Finally, the last book review is here. Actually, I have already read this book last January because I thought this was the book assigned to be reviewed at that time and I’ve also made an unfinished book review for it but when I learned that a different book was assigned, I stopped making the report. But at least now, I can continue what I’ve started.

The book entitled A Cabinet of Mathematical Curiosities, unlike the four others that were given before, was not a book with a definite storyline. It was filled with enjoyable games and puzzles that surely readers would have fun with. It is very pleasing and challenging at the same time which would surely improve and develop the thinking skills of its readers. Stewart was great in giving out elaborate discussions on the topics involved in the book where even ordinary readers are bound to be fascinated with. He was a very good mathematician because he managed to explain and discuss the book in the simplest of terms. This book is definitely my personal favourite because it was such a brain teaser.

The book opened up where Stewart mentioned that he had a notebook filled with problems in math when he was a kid. With this, it can be inferred that even at a young age, he was already a big fan of Mathematics (something rare in children nowadays). He then looked at Math in a new perspective, a more fun and enjoyable paradigm. He viewed it in a fun way so that he wouldn’t be pushing or forcing himself to learn such overwhelming topics because if you’re having fun with something, you won’t have a hard time in learning that something.  This then allows you to clear your mind and answer the problems immediately.

Admittedly, I didn’t get to answer all problems because it got kind of tiring but still, they were fun. If I’d have more time, I think I’d also have more patience to deal with them. However, I could say that this book can definitely improve one’s interest in Math because then people would be viewing Math in a fun way and the common notion that Math is like hell or very hard to deal with would be erased.

In this book, Stewart manages to deliver to his readers about his very long relationship with Math which started out when he was a kid. Through this book, the readers were able to follow through how a simple perspective or paradigm shift could change one’s attitude towards something. A Cabinet of Mathematical Curiosities, a great read indeed.

Mathematics Who? What? Where? When? Why? How?

“One of the virtues of knowing a bit of math is that you can impress the hell out of your friends.”

This quote is probably the coolest that I have ever heard from a mathematical author. Again, Ian Stewart has proved that not all of the curiosities lie beneath the universe: they are just suspended in numbers.

The book A Cabinet of Curiosities has given me a lot of insights about the puzzles that evolve around math: certain mysteries that has not been taught or learned, just analyzed and thought.  Not just the classic puzzles, but the new ones that can really boggle up minds. I am not quite the “thinking” type, but by just reading the book, it will present math’s other side of the coin.

Can you make a pop-up dodecahedron? How can you alternately fill a glass of water? Who tells the truth and lie? How can you extract a cherry from a glass? These are just some of the questions Stewart asked that he presented in the book. And the answers? One word: fascinating.

As the author mention in his introduction, you can skip at any page you like, but it’s more fun to follow the table of contents, for earlier problems are easy to solve than the on the proceeding pages, which as he said, challenging. But I think solving the first problem was quite tricky for me. I am referring to the problem Alien Encounter in which we have to identify the species of the aliens, one being always tells the truth and the other that tells a lie. I first encountered this problem in a math quiz bowl we have attended, but I was wrong about it. Seeing it again another time made me really think. Now I really kind of contemplated and when I flipped on the answer key guide, then again I was wrong. This problem may be not math-related but I assume, and is a fact that logical deductions are indeed of a necessity in the mathematical field.

Another problem presented in this book that I have already encountered is the River Crossing which involves a wolf, a goat and a cabbage. The player is the boatman and needs to carry only one to pass cross the river without the wolf eating the goat or the goat eating the cabbage. This is quite simpler since the wolf does not eat cabbage so the goat will be the first transported followed by either the wolf or cabbage. If one of the two were transported, the goat is carried back to the starting point, and the one being left will be carried back. The boatman returns to get the goat and voila, you solved a problem.

What’s unique about this book? I can say its uniqueness lies on the table of contents. As I skimmed through it, there were many chapters included but when you look at their pages, they are really short. The longest may be two pages at maximum. There are no morale, no story, no love, and no horror. Just mind-boggling g math puzzles, math anecdotes, and the one which I am not quite fond of, math jokes.

There are anecdotes in this book as well as jokes which generally, I don’t get at all. Either that they are so deep or I’m the one shallow individual. Either way, it was a nice thing that the author has mixed it up with this to avoid his readers being bored or tired of solving his golden puzzles. But having them, a kind of say “corny” jokes is a big no-no for me.

Reading the book, I can say that Stewart has offered small bits of math problems which are really a great exercise for the mind instead of serving a full course of x’es and y’s and complicated terminologies, graphs and figures, which I think is a “hooker” for an average, non-mathematician (like me… sssssshhhh….) reader.

This book has given me an idea that not all math problems are a bunch of boring stuffs you can pin a wall and shoot with a shotgun, but enigmas that can be synthesized not by just following a bunch of long, difficult formulae and can be solved in some little ordinary ways. What it needs are three things: interest, willingness and determination. After all, “There are three kinds of people in the world: those who can count, and those who can’t.”

A Book Review on Cabinet of Mathematical Curiosities by Ian Stewart

       The book was a not a novel or a story to read, but a valuable one made for us to enjoy in our leisure time. As people who are not Mathematicians, the book presents a lot of facts about the most popular facts, games and puzzles with the solutions purposely placed by the author for readers to understand them and be able to solve them. I was really in such awe when I tried to look at the solutions on the latter pages of the book. There are a lot of practicalities presented in each that I never get bored and made me crave to solve for more. It was also a great reference for me if I would like to impress some friends by knowing something really good about Mathematics. However, I would just like to highlight a few sections I just thought were really good: First, in our past learnings in elementary and high school we have calculated basic arithmetic in its standard form. However, the section on Curious Calculations amazed me on how one could calculate lengthy arithmetic in just seconds. Second, I have also discovered more from Pythagoras and his theorem commonly encountered in Trigonometry. Stories about Leonhard Euler, The Witch of Aghasi and Pierre de Fermat’s last theorem brought a lot of things new for us. Lastly, the geometrical figures such as the Greek Cross, The Sphinx of the Reptile and the Knots involving Topology brings one of us to recall one fond moment in a Molecular Biology class as true enough, topology and the mechanism of knots are evident in DNA since they are considered supercoiled most of the time.

Areas of Mathematics such as Algebra, Statistics, Arithmetic, Trigonometry, and Geometry are in the book and each are well-represented by problems. The book is good for everyone to learn while having fun at the same time. Had it not been for these Mathematicians who labored and have devoted their lives to Mathematics, this practical world would probably remain as one that is not understood by everyone. Indeed, they are amazing for making complicated things simple. 

Computers: A Written Report

I was a little bit worried when the group assignments were given during the first few meetings of Math1 since the computers group will be the very last one to initiate games, debate and a special presentation. I was thinking that our group’s presentation might fall during the hell week and that would be very unfortunate since a bunch of requirements, exams, papers, and etc. must be complied during that week. Luckily, my groupmates and I were able to manage our time despite the fact that we have to present seven days before hellweek comes.

The first thing we did was to play a game. It was supposed to be an outdoor one but the weather did not suit us well since it rained heavily so we have no choice. We utilized two rooms and three pairs from our group stationed in one room while the two remaining pairs used the other room. There were five stations having its own unique amusement and point system. The games played were all related to computers and these were the following: a.) typing speed which is a test for agility—how fast they could input characters on the computer; b.) icon/logo game in which each group was tasked to identify certain icons for two minutes; c.) unblock me which is a logical game; d.) computer history; and e.) computer trivia. The last two were mainly to test their knowledge about computers and it also aimed to reiterate information concerning computers. It was indeed a fun activity after all.

Our group had also initiated a debate pertaining to the topic “Illegal downloaders should be punished”. Majority of our classmates had reacted to this since almost all of them, “us” maybe are continuously doing piracy of movies and music. I was the whip of the government side and our main points on this matter are: illegal downloaders should be punished because they are breaking the law. Also, piracy is a form of stealing and it deprives the financial rewards that artists deserve to receive. Another thing is that it will threaten the economic growth because it is a fact that entertainment industry contributes greatly to the national revenue. However, the opposition side emphasized that illegal downloader should not be punished because of practicality reasons. Almost all people are doing this so there would be no enough prisons to punish these people. Another point is that it will encourage popularity of artists and it is also cheaper. Still, during the first and last tally of votes, nobody was in favor for the punishment of illegal downloaders. After the debate, our group had shown to the class a 15-minute movie presentation. It was all about a murder case of a school teacher. And the antidote was the utilization of computer softwares such as BLAST and DNA Analysis software in order to trace the serial killer. In the making, our group experienced a lot of fun because of some bloopers and we did some weird acts that we were not used to do in our normal lives.

In totality, it was a great experience being in the computers group and a part of Math1 class as a whole. Although I am the only upperclassman majoring in biology, I was still able to relate and mingle with my classmates especially to my groupmates. I was also very happy that this group activity was a success. Thanks to everyone! J

                                                               

Without Tears

When I read a book or watch a movie, I try to read its reviews first. Mind you, it is the reviews and not the summary. I don’t do it to cheat. Instead, I find it helpful in knowing what to expect of the book or the movie. I want to know if it’s worth my time and if I am going to learn new things. So, I try to search first. Unfortunately for this book, I wasn’t able to read a review. And so, I don’t really know what to expect. I don’t know the topic or if the book is great.  The only thing that I know of the book is it has a nice title and cover.

Reading the first paragraph of the introduction of Len Fisher’s Rock, Paper and Scissors, I learned that it was about game theory and its connections to everyday life. I really don’t know a lot of things about game theory.  The later paragraphs help me to understand more about Game theory, which is not only a mathematical science that studies the strategic decision making. It is also that the results of the strategies depend on the other people strategies. Also, it is specifically about mathematical models of conflict and cooperation between the makers.

  Fisher continued more with game theory and its applications in the next eight chapters. Fisher provided examples of game theory. One of these is the Prisoner’s dilemma in which he described in chapter one. I find it really cool. The prisoner’s dilemma can be applied in all areas. Like in the book, it can be with few boys having the same crush to the supermarkets and marketing. He also discussed Nash equilibrium. He said it is a logical trap. I find Fisher’s view on Nash equilibrium a negative one. In the second chapter, he told the story when he was a kid and the trouble he caused. His idea to minimize the consequence is an application of the minimax principle. Fisher also gave another example with the meat and the elder sister.  He then explored this subject more with its concepts and also he discussed fair division.

The third chapter is about the seven deadly dilemmas. They are the seven of the most interesting game theory problems. Fisher gave an interesting exploration of each seven dilemmas. In the seven, one that I like the most is the chicken. Somehow I can relate more to this. The next chapter is for me, the most exciting one. It discussed the game rock, paper and scissors. Rock, paper and scissors is more commonly known as bato, bato pick. I used to play it every day when I was a child. To know more of the game is exciting, I find out that there is no really strategy that is better or that would dominate. Random choices are better in playing this game. Also, I found out that the simple game of rock, paper and scissors can be used in other conflict situations.  The next three chapters of the book discussed more about getting together and trusting each other. In other words it is cooperation and communication. It discusses more strategies and approaches that can help in preventing the consequences of the prisoner’s dilemma.

As I read the book, I realized that game theory is everywhere. From the simple game we all have played to the conflicts and problems we have encountered in this world. It is also interrelated with biology. Game theory is used in biology. Biologists used it in understanding cooperation in the survival of the fittest. Also, he mentioned some scientific experiments used in the game theory. I really appreciate it that he included some biological experiments and examples. As biologists, it helps us understand more things and broaden our knowledge.

Now that I finished reading the book, I realized that it was good that I did not have any expectations. I wouldn't think that it would be met. The book was simply amazing. It may have some dry and slow moments, but overall it was fun to read. The author discussed things without causing us to bleeding in our nose or tears running down our face. And, he also gave us a few laughs. In other words, the book is simple and light, cheerful and humorous.  It was also a fascinating guide for math people and dummies like me.  Also I learned a lot of the given problems, dilemmas, history and science. Len Fisher is a good author. He did a good job on the book. He fascinatingly and with enlightenment explored the world of game theory. He also accomplished his goal of discussing game theory and its connection to everyday use. I would recommend this book to anyone who loves games, science and math.

Farewell to Curiosity

               Speaking of Hersh, he has yet completed another masterpiece written by his hand and inspired once again by mathematical cataclysms and foundation of ideas as he has always been. Professor Stewart’s Cabinet of Mathematical Curiosities is certainly holding true to its title. When I read this book, it doesn’t even start with an organized table of contents. It’s not even a table of contents if I’m to judge it visually and technically. It’s a list! It’s not just an ordinary list containing incomprehensive phrases.

               As I read along the pages of familiar formats and fonts as in Hersh’s other book that we first made a book review on, I was slowly beginning to understand the book. It’s not a book of characters and plots and plot twists. It does not connect or interlink previous and next chapters. So basically, it contains all that can be read in a mathematical perspective. You there, gamers and logic lovers! This book’s for you. It’s interesting, those different games. Added to that are follow-up questions on various and highly diverse topics which are significantly rooted on old and new mathematical principles and theories alike. There are a lot of games to choose from, you don’t have to start and proceed in a chronological order. Pick at random and you’ll see that anywhere in this book, you’ll be sure to get away out of boredom’s way. You’d be killing time all through summer, if you’d like to put it that way.

               Finally, I can say that this book summarizes the previous books we reviewed. It reflects all the information, points and stories of the mechanisms explained from previous books. All the teachings we got from those mathematically related books are applied in this book. It’s as if it takes you to testing your knowledge of how much you’ve learn so far besides and beyond the conventional mathematics we’re taught. Nevertheless, each game profoundly explained all its questions and answers. Yes, it holds answers which are concentrated on the last chapters of this book. Honestly, you’re going to appreciate more of all that you learn as you see them came into action by participating with the mechanics and instructions of this book. This is really fun. Some are a bit challenging and that definitely adds to the thrill of reading this. Aloha! You've got the key to every lock in this book. Enjoy and say farewell to curiosity.

Behind the Magic Trick

Save the best for last! Ian Stewart yet wrote another book that is fun, enjoyable and with attempt to make the readers fall in love with math.  This time he compiled tricks, problems, puzzles, brainteasers, facts and jokes which he calls “curiosities” in a notebook he’s been keeping since he was a kid.

I would have to admit that most of the problems I did not get to solve, and some I just skipped. And that it was getting tedious going back and forth the answers page. Solving it correctly is a very rare case, in which instances I’d find myself ridiculously happy. My favourite one was the sliced fingers. It took me an awful lot of tries that when I finally got it, I didn’t want the string removed from my hands! I just understood topology a tiny bit more than I used to a few moments before I read the book.

Not everything is new. Stewart also tackled about the classics such as the Fibonacci numbers, why we can’t divide anything by zero, the sausage conjecture. All of these concepts I have heard before, but not as well explained as it was in this book.

There was also something about the way it was written that would make the reader find the enigma interesting.  Like how the Great Whodunni and Grumpelina are more palatable starting points than A and B. seems completely random and unrelated, but they sure are otherwise. Also, the entries are usually short (except for that global warming part) which captures my short attention span quite well.  Somehow because of this, the information is reduced to bite-size that makes it easier to digest.

In totality I find the book like watching a magician perform a trick and then he tells you how it’s done afterwards (something that doesn’t happen everyday, does it?). The author has that writing aura that makes the reader feel like he’s just a friend telling a story, not a professor trying to teach math. I may not have developed the love for math like the author did, but I just started to realize how interesting it could be outside the math I’ve always known, the one with often inexplicably hard structure with strings attached to grades.

Statistical Probability of Passing or Not

        Statistics make research, surveys and data analysis easier and way more understandable. Imagine research without statistics, raw data being analysed manually and piece by piece, biased judgement for the error and significance of each value and the wasted effort and time that will be spent. The importance of statistics may be neglected at times but its usefulness is evident, although sometimes, unnoticed.

            Through Math 1, I was able to appreciate statistics in a deeper sense. As the members of the group ‘Statistics’, we were able to review some statistical lessons to the class through different activities such as games, film viewing and debate. For the games, we conducted an outdoor activity in which the class was divided into their respective groups and had a race to every station to answer several questions related to statistics. As for the film-viewing, the movie was made and produced by our group in which each of us was able to participate. My part in the story was exciting since it would be my first time to act in front of a camera and that it is out from my usual character. I was Serena and I was the antagonist in the story, a killer, more specifically. The filming was really fun and even with the busy schedule of each member, we were able to finish it early although the editing part became the problem because of its long rendering time. The debate has the topic of whether the statistical poll is reliable or not. At the end, the opposition won the judgment of the audience.

            Through these series of activities, not only the importance of statistics became clear to me. But also the friendship, cooperation, understanding and patience for each and everyone became clear that it is very important and the key for the successful presentation and the possible way to pass the subject, in general.

3 C's; Cannot be Contained in a Cabinet

There are three kinds of knowledge. One is what we obtain from school, second is what we get from other people and lastly the knowledge that we ourselves unknowingly learn. Stuart was one of the peculiar guys whom I admire. And Oh, by the way I meant awesome peculiarity.

I myself have been filled with curiosities and good thing that the world can satisfy it. I like the line from Ian’s book “The math you didn't do at school is interesting”. Indeed learning without pressure on taking tests is the ultimate way to genuinely gain knowledge. Every time a gap in me brought by curiosity is filled, I feel that I’m walking on air. What I find in the author of the book similar to me is being able to see things at a different perspective and not limiting my education to what is known. The book gave me an insight to what math is outside of the box and not the creepy subject to be feared about. Math is about putting things into places in their perfect fit just like managing things inside a cabinet.

The first chapter was my favorite since it was about aliens and I am forever interested in extraterrestrial life. His hypothetical story about two men encountering aliens was impressively nerdy and I liked it. The question represents logic that is applied by twisting truth and false. I enjoyed finding whether Alfy, Betty and Gemma were Gibberish or Veracitor which are groups of the same species determined by how they tell statements based on truth. I will admit I really got puzzled.

Puzzles and games are a part of everyone’s life. His examples are entertaining and not to mention he had incorporated math together with humor. There were so many interactive games concerning patterns and puzzles that are challenging. I think school math should be more interactive, innovative showing the creativity that can be found in math. Games include probability, geometry (my favorite) and logic. For example a pop up dodecahedron, one is  how to extract a cherry from a cocktail glass which is hard as drinkers say and the true reason why you can't divide anything by zero. There were even some tips to make money just by proving the obvious; yeah I know it was hilarious. As a biology student this book presented math as something to look forward to everyday, even in our metabolism math is used.

Mathematics uses logic and philosophy as well, that’s why without a doubt it contains a lot of uncertainties. These uncertainties are also brought by curiosities where the latter brings knowledge that we use in our everyday lives. What I admired in Ian Stuart was that he shared his collection of ideas since he was 14 years old, as early as that and didn't just keep it on his own. This book was really made with passion and love by the author since it reflects his insights and journey in meeting mathematics.

In the end life is a cycle meaning it revolves in patterns. Equipped is our cabinet without any corners that will be filled by knowledge that is infinite ∞

Logical Thinking at Work

            Mathematics is logic. It is not just about the numbers, shapes and equations but can also go beyond the four-squared room and can be at every part of the society and life of each person. Without knowing it, we may already be inside the area of mathematics as we live our normal life everyday. In the book of Ian Stewart, the ‘Cabinet of Mathematical Curiosities’, he was able to share some of his views and personal entertainment that involve his creative and mathematical thinking. The characterization of logic in the field of mathematics and how numbers and analysis be equal to fun were some stuff that can be derived from this book. Generally, the book contains different puzzles and games that can give you entertainment and at the same time challenges which can measure the level of your analytical and understanding skills.

            At the start of the book, aliens were able to invade my mind and immediately went into space. How can you even know which is which with only some questions asked? Well, Capt. Quirk found a way to analyse this problem. Even with this simple puzzle, it was able to make your brain work into several analyses and do imaginative works of patterns and relation of each statement.

        As the book go further with its puzzles and games, different historical names in the world of mathematics were mentioned such as Fibonacci and Fermat. The works they were able to contribute were described and used in this book in a way that it is not technical yet understandable (thanks to the writing skills of the author). I can say that this is mainly for entertainment yet at the same time touches some bits of mathematical concepts.

             One amazing thing about this book is that, mathematics was made friendly and fun for those that are not really a fan of it. Reading some of the problems, I observed that sometimes, numbers were not even included just to achieve the answer. As for those that involve numbers, such as his explanation as to why we can’t divide a number by zero, he was able to explain the concept in a very simple and understandable way. This is one of my favorite because, personally, I am one of those that do not understand this type of rule in mathematics. Well, 0/0 was also not considered applicable since it is unpredictable and as Stewart said, causes headache.

            The mathematical concepts were made understandable by the problems and questions since the mind itself is the one doing the thinking which is apparently out of the traditional way of learning. Yes, answers were given at the end of the book but the urge to answer it and to feel the satisfaction of solving something drives an individual to think more about it.

            In his introduction, he mentioned that some of the puzzles in this book were compiled when he was still 14 years old. Relying in this statement, it can be concluded that even at a very young age, he is already fond of mathematics which, in my opinion, is very hard to find nowadays in the pool of youngsters in the community. With this book, the interest in math can be developed because of the different perspective it gives to the readers about math. It is more than just the complicated stuffs it solves involving numbers and variables but it also has its own side of fun and mind games. Without knowing it, we already start to appreciate math in its own fun way.

            Ian Stewart was able to share his cabinet of puzzles and games. Some may say that this book has no story or plot but it actually has its own story to tell. It is all about the tale of how logic and analysis affected the life of one person as it is one of the factors that molded him into someone that he is today. A lover of mathematics and a great writer.

The Fun and Amazement Simulator

By: Kissel Cablayda

Playful and witty- The Cabinet of Mathematical Curiosities is a must read book for all ages. Of the five books given to be reviewed, this is the book that finds the reader to be unexpectedly time and effort engaging, however, in a way that it lures the readers to play and play game after game. This is a collection of tricks that are perfect for those who believes that math is a magic, a collection of games for math gamers, and a collection of ice breaker for those who just want to kill the time. Ian Stewart, as a witty author as ever be, never failed the readers to engage his readers to the trickery of math curiosities.

His smart tactic to use universal emotions of human, such as curiosity, fun and humor is a wise way to subtly connect and develop the readers’ interest in math exploration and appreciation.

One of the most enjoying parts of his game collection is the “more curios calculations” part in which one doubles a three digit number divide it by 7, then 11 then 13 and then one gets the same three digit number as the answer. The wise way of those who have discovered this trick is a skill that can lead the “player” amazed and confused at the same time. This kind of mathematical generalization is just one of the many tricks that keen observer can do and re-enact to others. Such algebraic game is good for the brain. It is a good example to encourage one person to think and dig deeper about the situation behind the trickery. Thus it is safe to say that the author encourages the readers to become a detective- a detective for mathematical confusion and trickeries.

Among other games, the book also included mathematical facts that leaves the reader information that would astonish them thus even inspire them to become a math enthusiast. A very god example is Ian Stewart’s story about the German algebraist Ernst Kummer and his inability to solve mathematical equations. However Kummer is a notable genius that had contributed some of the best works on Fermat’s theorem. This short story would really make the reader realize that you don’t have to be a math genius to become a mathematician, in fact you can be famous in this field as long as there someone who you can rely on when you need basic calculations.

The book is indeed a good read, a good interest and amazement simulator. Thus, this should be a good peg and an inspiration to those who attempt to invite the audience to engage in different mathematical concepts and theories.

The Puzzles to be Solved

Ghad! I‘m so glad that this will be the last book I’ll write a review about. At least, the last book is somehow interesting and enjoyable. The book is entitled Cabinet of Mathematical Curiosities which is all about mathematical games, puzzles and all other mathematical tricks. Those that were mentioned are the things he call curiosities. The author, Stewart, discusses the history of mathematical things in a way that the readers can understand what he wants to relay.

The book does not tell a story with mathematics in it unlike the A Certain Ambiguity and it also doesn't explain some mathematical game theories unlike the Rock, Paper, Scissors. It is just a book wherein puzzles, games, jokes and tricks are collected (but especially, math is still related to them). You don’t need to have a large knowledge about some math branches like statistics and calculus to understand the book. It is just about analysis and logic. I enjoyed the book even if I didn't answer all the given puzzles.

The book revolves about mathematical logic, geometry, probability and plain Jane arithmetic. He also mentions facts like why anything cannot be divided by zero, the seven bridges of Konigsberg (the one that you must find a path that can pass all the bridges only once) and the sausage conjecture (where how efficiently can circles or spheres be wrapped).

The thing that really made me happy was the “Make Me a Pentagon” in which he asks his readers to make a pentagon from a strip. Well, I already knew this one because I once loved making paper stars and the very first step in making them is to make a pentagon. Then there was it! I just felt so proud about myself (haha). For those who didn’t know how to make it, logical thinking and analysis are a requirement.

Another cool thing was the Extracting the Cherry where only 2 sticks are allowed to move when extracting the cherry from the glass that was made of 4 sticks. This was just exactly the same as the one that I knew. It only has different subjects wherein the cherry turns to be a poop (haha disgusting) and the glass turns to be a dust pan. This trick, I think, was the very first trick I’ve ever known in my life.

Next was the Empty Glasses wherein 5 glasses having 3 full glasses first and 2 empty in the last will be arranged in an alternate manner (full-empty-full-empty-full) in which only one glass is allowed to move. I admit that I really didn’t know how to solve this one because I was kind of dependent on my previous favorite tricks in which I knew how to solve them already. This was very tricky but when I found out the answer, it was just very simple and it just requires your common sense. Nah, it makes me slap my face (haha).

Actually, I haven’t finished reading the book because there’s no more time to do it. This book review is needed to be passed today even if we were given months to read this but I really can’t handle both the studying and the book reading. I want to finish this since summer starts now. This book is really interesting and fun. I could share the tricks I’ve learned to other people. It makes you realize that analysis is really very important. Some tricks and puzzles were fun though but I only mentioned those that were really cool for me. I want to congratulate the author for making such an amazing book.

And this is how I end my last book review :) thank you!

The Cabinet of Never-Ending Dreams: A Book Review of Cabinet of Mathematical Curiosities

The book Cabinet of Mathematical Curiosities was written by Mr. Ian Stewart. The front cover itself looks interesting and appealing to the eyes. We all know that colorful covers on books are attractive and the book never failed to do so. The book’s content is composed of puzzles, games, and problems, and mathematical jokes. The book is reader-friendly and may attract people of different ages. It is a good book for someone who wants to delve in the mathematical realm or someone who just want to have fun.

            Though the past weeks was sucking the energy from my body, it managed to bring smiles and delight to me. The images coupled with various interactive games, quizzes, and puzzles had sparked my interest. Stewart discussed the topics related to mathematics by making it be easily understood by the readers. It really takes a mathematician to write an audience-friendly book. Mainly, the book also tackles the adventures taken by Stewart when he was on our actual age. Unlike the first books I read, this book was deemed to be fun.

            The first parts of the book discussed how the author had a notebook stuffed with mathematical problems. The author took the mathematics in a fun way instead of forcing himself to study those equations and formula. He stressed that mathematics should be fun as it promotes less stress and encourages our mind to think clearly. Thus, it leads us to answer our inquiries. Interestingly, Stewart spent years filling his own cabinet containing with lots of mathematical games, puzzles, stories and jokes. Even his adventurous mind was carved in this symbolic “cabinet.”

            The cabinet, similar to a treasure containing with rare jewels and enormous wealth, contains games involving the use of logic, geometry, and probability. Some topics featured in the books is the formation of polygons using match sticks, a pop-up dodecahedron, and the mystery why we can’t divide anything by zero. It was my first time to learn some of the problems discussed by Stewart. Example is the problem with the string, where it was tied as a loop and then looped around the fingers. Stewart explained that once it was pulled away, the outcome is that the fingers will not be entangled. Yet, I was fascinated with it. I even attempted to do it but unluckily I ended up with difficulty.

            I love geography. I like how I ended in exploring cultures and other areas by just reading books or performing researches. In relation to geography, Stewart introduced the color maps. There is a way on how to color maps so that nearby cities will have the same color. However, I find this one tricky since I am not fond of maps having one color only [except for statistical analysis such as outcome of elections (e.g. US Presidential Elections.)]

            One of the most popular games played in relation to match sticks (I know, handle with care) is to use them to form polygons. This game was already encountered in the game activity introduced by the Geometry group last February. In this game, set of match sticks are connected from one another. In a given number of moves, the player must form new polygons. I admit that I am very slow when it comes with these types of games. However, I can accomplish a given puzzle to me. A player exemplifying a degree of dexterity is advantageous for this type of game.

            The succeeding chapters provided other games. Among Stewart discussed is the knight’s move in a chess game, the pop-up dodecahedron, Pythagorean triples, the reason why we cannot divide any number to zero. I also got back the glimpse of the Poincare conjecture the chaos theory and the P=NP problem which offers a million dollars who can solve the problem. These topics were already discussed on the last series of the “Story of Maths” by Professor Marcus du Sautoy.

            The bridges of Konigsberg, which was already tackled again in the “Story of Maths” came back in the scene. Stewart elaborated that when a bridge’s path has been traced, it should have the possibility of having even paths.

The Pythagorean triples were also introduced. I have never heard of this topic, making it difficult for me to decipher what it implies. Another game in the book is how to connect the wires without crossing each other.

Overall, the book opened me to the other wonders of mathematics.  My time in the past weeks almost prohibited me from reading the book. It helped me lift my spirit as it allowed me to reminisce how fun to be a child again, where fun is the only world revolving around them. Every game is like a riddle where it challenged me to think deeply and the answer was very simple. This kind of book is what the readers need to start loving mathematics. I am amazed how Ian Stewart managed to form short stories and puzzles from his “cabinet.” The cabinet is not just a furniture left to stand; it became the pillar which revealed the existence of Ian Stewart’s childhood and the fun he had with mathematics. Collection of these ideas is tedious and I commend the author for his dedication for mathematics.

The pages of the book contained with wonderful imagery coupled with fine texts of explanations were properly managed. I really enjoyed reading the book. I might go back reading the book and answer all the puzzles, quizzes, and games contained in it.

How Do I Undo the Past?

            Oh no. The title sounds overly melodramatic. But really, Ian Stewart, bakit ngayon ka lng dumating sa buhay ko? (Flaaashback!)

            March 28, 2014. Hours left before the deadline for the last book review. Scan here; read there; the ink of pen started to leave its footprints on my paper. At first it was a burden I thought I’d never carry through, but then it turned out to be, yes, still a burden, but a beautiful burden. J

            I’ve always had this unjustified (yes, I admit -_-) loatheness towards math. Math and its cruel twists. And surely, your impression towards a thing really affects your perception with it. I have perceived math as something so harshly essential in your life. Math is a “DO or DIE” thing. And since I have seen math this way, it has, in return, treated me the same epic way. I don’t really know why I hated math. Did my low grades cause my hatred or my hatred caused my low grades?  And have you noticed that I used the word “hateD” (again, hateDDD)? That’s all thanks to Ian Stewart’s Cabinet of Mathematical Curiosities.

            This masterpiece of Ian Stewart really did change my impression towards math. The book was filled with his treasures in mathematics: puzzles, riddles, short stories, concepts, and many more things that he found worth-keeping and of course, worth-sharing. This is not like the other books in mathematics that will make you doze off. The puzzles in this book really would catch and keep your interest. ;) Sad to say I was not able to entertain all puzzles due to time mismanagement. But really, I never thought I’d have fun in solving the puzzles and brainstorming the riddles. The author did a good job in converting complex and boring mathematical exaggerated equations into simple and easy-paced words. The complicated equations were more interestingly and comprehensibly molded into puzzles and tricks that unfold the beauty and simplicity in math. With this book, I had learned to see math not as a boring, life-sucking demon, but as kind of like crazy-fun friend. How I wish I had read this book during my childhood days, when time was so cheap and reading books sounded so cute.

            To all those mathematically freaked-out dudes out there (like how I used to be), I urge, entice, and push you to really take time to read this book. Though the intensity of benefits might vary, I assure you that it will make learning math in your life more fun and a little less of a burden. And lastly, they always say “save the best for last”. Indeed, this book deserves to be the last. J

A Certain Ambiguity

Kissel Cablayda                                                                                                                      

A certain ambiguity is a novel that tries to lure the audience with mathematical and philosophical ideas through tailoring it into a not so dramatic story. Suri and Bal’s serious attempt to bombard the story with the different notions about math connecting it to a story of a grandson trying to search for the reason for his grandfather’s imprisonment is not a very persuading strategy. Thus it just made the story a long and dragging presentation about math. Hence the value of art and making a story was compromised.

The story revolves around a grandson, Ravi, who was inspired by his grandfather to pursue a mathematical dream they both love. A few years after his grandfathers’ death, he flies to from India to America and pursued his study. He takes up a liberal arts mathematics undergraduate course at Stanford, where he meets friends and teacher who shares the same interests in mathematics. And there the search for so many mathematical ambiguities starts to developed through a long and uninteresting discussions about infinity, cardinality, power sets, Euclidian geometry and etc. In the middle of his search for mathematical enlightenment he finds out that his grandfather was jailed and there he tries to find out why.

The part where the story turns out to be less interesting is at the classroom setting, where they talked and debated about infinity with his friend, his professor and his classmates for a very long period. This is the part where the readers are starting to have that “ooops! Nerd alert!” feels. Those endless dialogues can convince the readers to put down and shut the book close.

However, the grand attempt of the writers to have a unique novel didn’t lure much of the in depth interest and thus making the readers disappointed. The fact that they came up with a unique idea to connect math and literature is smart. It is enough to take the attention of the readers to buy and avail the book. However, this is not enough for the readers to engage and to scan the book up until to its last leaf. Its sound and innovative attempt is just a disparity to produce a sophisticated story and an in depth presentation of mathematical concept.

What makes it so dragging is that after a short introduction of a story setting, the overused pattern of which they talk lengthily and presenting an investigation of mathematical in long pages makes the reader to have an information overload and a tardy digestion of the mathematical ideas.

If it were presented in a way that there has a balance among mathematics, philosophy and modern literature, the story might not compromised the story and thus leaving the readers less disappointing.

            If the authors would have sustained the same feels in the introduction part, were math and drama somehow fits perfectly, especially on the part of Ravi’s mourning of his loss of a grandfather, then the story would be more interesting and thus they would have achieved the kind of novelty they attempt to produce.

A Glimpse to Outdoor Mathematics

          When I have started reading the book, it appeared to me the Ian Stewart was a genius because he decided to keep a notebook only for math. I didn’t even think that there is fun in mathematics or even mathematics outside school at that age. He insists that there is more than mathematics than there is inside school and to what our teachers have taught us. In that notebook of his was a collection of riddles, puzzles, games, and fun thoughts of mathematics. It was too many I think that he needed to publish this book.

            His passion of the games, puzzles, riddles about math was very emanating in the words he uses. You can really feel his excitement as he shares to you those. The book has logical puzzles, geometric puzzles, numerical puzzles, probability puzzles, and some are simply mathematical jokes. Some of these are really fun but I should admit that I couldn’t fully grasp other concepts. I like what Stewart said when math can both impress and annoy people in numerous ways. That was very true. I also would like to acknowledge his choice of words; it was understandable.

            Puzzles included in the book had answers at the latter part. It was mind boggling and annoying that the answers were not after each problem! However, it was nice that the author also included problems that are unanswered proving that mathematics is not completely done and that there is more to it, more problems and curiosities to be solved.

Though there are a lot of problems that have high level of difficulties, mathematical jokes are mixed throughout the sections of the book to uplift our spirits at times we do not understand a certain puzzle.

            The author was successful in showing lots of amusing stuffs about math, many of these we don’t know. He also tried to stimulate our curiosities about outdoor mathematics.

Pirates of Silicon Valley: A Review

Pirates of Silicon Valley is a 1999 film directed by Martyn Burke. It was based on Paul Freiberger and Michael Swaine’s book: ”Fire in the Valley: The Making of Personal Computer”. It was about the competition between Steve Jobs, the creator of Apple and Bill Gates, the creator of Microsoft. Steve Jobs was portrayed by Noah Wyle and Bill Gates with Anthony Michael Hall.

The film showed the two characters roles in real life and how they faced struggles in their personal lives and the problems they had in their own companies.

 Steve Jobs started making computers with his partner, Steve Wozniak in a very small garage. While Bill Gates started making computer softwares  in a motel warehouse.

Steve Jobs has an excellent performance in Marketing. But when it comes to treating his employees, he treated them poorly. Bill Gates is more relaxed and easygoing when he treats his company workers.

As we could see from the movie, Steve Jobs and Bill Gates worked really hard for their companies to be successful. They marked their names on history out of blood and sweat.

Apple is more on creating computers (and now including smartphones and other gadgets) while Microsoft is more on creating softwares that we have and use on our computers.

A part in the movie tells us that Bill Gates stole Jobs’ computer ideas, making it a new design and selling it as his own. Because Gates stole his information, he became very successful and eventually became one of the richest man in the world.

Because what has happened, the two companies became two huge rivalries and until now have not gained each other’s trust.

To be honest, If I were given the chance to rate, I would give this one a four out of five. I am not into computers the reason it is not that interesting to me. But in the bright side, the movie is very informative and I really appreciate both of them for making our lives better today.

NOT YOUR ORDINARY SUDOKU ( A book review on Ian Stewart's Cabinet of Mathematical Curiosities)

            I was surprised when I opened the book. I thought there is some kind of scientific fiction going on in this book because when I read the title, “Cabinet of Mathematical Curiosities”, the first thing that entered my mind was the idea of Narnia where there is a closet that can lead you to this magical place. But okay, I was totally wrong. It was actually about the puzzles, jokes, and stories constructed by the author Ian Stewart which are organized in this “cabinet”, the book.

            I can describe this book as genius. It is very different from the past reading materials in Math 1. It provides a holistic point of view in Math. It does not just feed concepts in Mathematics which is something that most of us find annoying. What it does is feed us Mathematical concepts in an entertaining way. Despite those jokes that are not even funny in any way, this book is innovative. It even incorporates philosophical concepts and experiences of the author. It also provides some “life hacks” that can be used in calculations that are totally helpful to students. Indeed, it is like an all-in-one book.

            I admit that I did skip some pages when I read the book. This is the advantage of this book for some readers. You can read random topics only and still not miss the flow of ideas. You can read one topic each day or whenever you want and you can ponder on it for days and have some build-up of opinions about the topic. I also have some of my favorite topics in the book and favorite puzzles that made me get a ballpen and a paper to try to solve it. The book really lived up to its theme, “curiosity”.

            One of the topics that left a mark in my mind is the “Rabbits in the Hat”. I never thought that magic can be associated with Math. I also never thought that calculations would be involved in misdirection, one of the main techniques in the field of magic. Now, I’m starting to think magicians are actually in mental chaos when they are performing magic tricks.

            Another part of the book that got me is those curious calculations. I even took my calculator from my bag to check if the expected results would really be achieved. It amazed me that it did. However, the author said that these calculator tricks are actually made from generalizations and careful evaluations of the algebraic properties of numbers. Any person can make these calculator tricks if only he/she has fully grasped the concept of algebra.

            I also find the philosophical ideas of the author very interesting. That of the “Heron Suit” was my favorite. It reminded me of the famous philosophical idea which is “the black cat in the dark room”. The philosophical excerpts in the book from the author just showed how well-rounded he is. It also showed the views of mathematicians towards philosophy and analogy.

            In terms of humor, this book didn’t also lack one. Though some of the jokes were not really funny in my point of view and though it got me saying “Huh?” after reading them, they gave me an idea on how mathematicians perceive jokes and construct jokes. At some level, they are nerdy yet if a person reads them again and again, you’ll figure out that there is humor in it. This gives substance to the book.

            The book is, indeed, comparable to a cabinet. There is a drawer for challenges from puzzles, another drawer for humor from the jokes, another drawer for experiences from the stories, and another drawer for adventure from the games. These drawers and compartments makes up the entire cabinet which is filled by the parts of the author’s self. As I read the book, a part of the author’s self becomes a part of me too, in some ways, which is why I liked the book. It is not just a book of puzzles, jokes and games. It is a book with substance.

           

Statistics: Written Report

                   Last February, we filmed a movie with a mixed genre of horror, drama, and comedy. I played the role of Lourdes, the mother of Deevina which happened to be dead. The story was about Nardo (Jayson Cardillo) who tries to find the true story behind the death of Deevina. He was taking everyone in the office as the suspect. Drei Yucamco, who played the role of Gardo versoza, was the boss and he was very much in love with Deevina. The last time he saw her was with another man making him very angry and a very good suspect. Hianne Khua played the role of the current girlfriend of Gardo. She was very envious of Deevina because Gardo was still in love with her. Near the end of the movie, Nardo was able to know who killed Deevina using Statistics, of course. It was very funny when the whole class has watched the movie because we just tried to insert the concept of Statistics in it.

           We also conducted games on the CSM grounds. However, I was somewhat disappointed because not everyone participated happily.  I think it was because right after our Math 1 class was our Biochemistry exam. I just hoped some of them enjoyed. Lastly, during the film showing, we debated on the notion of “Statistical polls are reliable.” I was the prime minister of the government side along with Drei Yucamco as the deputy prime minister and Hianne Khua as the whip. The class voted to which group they are for and apparently, the opposition won. Overall, everything we did was fun and worth it.

Not Just Typical Puzzles: A Book Review on Ian Stewart's "Cabinet of Mathematical Curiosities"

            It’s perfect book to end a stressful semester. Basically this is my last requirement for this academic year in UP, thus, I should enjoy it. I did! Cabinet of Mathematical Curiosities by Ian Stewart was the most enjoyable one among all books I have read for book reviews. At first I thought it will be another typical nerdish book that goes into deeper math, however, it was the opposite of everything I have thought. Honestly, it wasn’t stressful to read at all. You’ll just catch yourself enjoying the book and you wouldn’t just mind what time is it.

            The author started by introducing to the readers the concept and idea behind the title. He stated that “Curiosities is a sample from my cabinet, a miscellany of intriguing mathematical games, puzzles, stories, and factoids” and this statement has reflected the series of fun that overflowed on the book. He then started the flow of the book. Reading along, I have already encountered some of the games, tricks and logics written. The logic of “Difference triangles” has caught my attention since it was my first time to read and learn on this. It is crazy to think that this simple trick or logic has deeper concept behind as apprehended by mathematicians. Continuing, I have observed how patterns are present in almost all these tricks. Thus, this vibrates that mathematics, in any form is indeed the science of patterns. He was truly right when he said that “the mathematics we did not learn in school is more fun”.

            “Extracting the cherry” was indeed a tricky one though if you’ll know the answer, you think you’re just fooling yourself around. I have experienced to play this game since high school and if I haven’t looked at the answer on the book, I swear, it will take me hours to guess it. “Make Me a Pentagon” was also a good one. I have deduced that these previous two games that I have mentioned require two things: logical thinking or luck. Well, I think it isn’t game of luck but it implies analysis. Now I laughed at “Empty Glasses”. I was critically thinking how to answer the game, yet all you need is common sense! I remember that way back home, my brother used to have these tricks and throw it on me. And yes, I can’t answer these easy tricks since al I thought was that it needs intelligence.

            Going through, I stopped at the “Compensating Errors” entry. I remembered having this type of question during mathematic quiz bowls in high school. I like this entry since you should use your brain to answer this. Also, I believe everyone will agree that the feeling of answering this type of question is just indescribable! The logic of true or false has always been my weakness. And here we go on the entry of “Spelling mistakes”. The statement was “‘Thare are five mistukes im this centence.’ True or false?”. Now I have again analyzed this logic trying to figure out the correct answer so that for the first time, I can be able to answer true-or-false logic  correctly. As expected, I failed. I have not included the claim that there are 5 mistakes in the statement as the 5^th mistake. Maybe next time I can guess or answer correctly.

            As I move along the book, I felt really interested on each entry. However, there are some entries that I quite skipped. The reason is that either I have already encountered it or it’s just that it’s quite too long to read and comprehend. Moreover, I still looked for some that could astonish me, omething that holds both analysis and common sense.

            “Don’t let go!” Okay, maybe this would be it. I tried to not look at the answer on the answer key. This segment is all about topology which deals with shapes, thus, geometry is involved. I believe that this should include imagination, especially the fact that I don’t have any rope in this coffee shop that I am in right now. Somehow, I got it right. My body has involvement to the answer to the topological theorem. Though I didn’t get the answer directly and accurately, at least I had the hint on my mind.

            Allow me to discuss one last segment before generalizing my ideas and thoughts on the book of Ian Stewart. Since I am interested to philosophy, lastly, I will include in this short review the entry “Logical or Not?” I thought I really had to review the principle behind statements being logical or not. Basically, I really thought it was not logical, and I was right. The problem was that I wasn’t able to think why it is not logical. Thus, as an answer to my question, I read on page 288 for the answer. Amazingly, it included some arithmetic to further prove the sensibility of the statement.

            Other puzzles were indeed fun. However, I have only included those I am interested the most in this book review. Indeed, it was a fun book to read upon. The author was successful on dealing with the readers. I also thought that I can use some of the entries to play with my cousins. Moreover, the book did not just address fun and playing with logics, but also the idea of mathematics as well as patterns behind these mathematical puzzles. With this, I end my Math 1 course in UP with a smile. J