“As it is, the book is indispensable; it has, indeed, no serious English rival.” — Times Literary Supplement “Sir Thomas Heath, foremost English historian of the ancient exact sciences in the twentieth century.” — Prof. W. H. Stahl
“Indeed, seeing that so much of Greek is mathematics, it is arguable that, if one would understand the Greek genius fully, it would be a good plan to begin with their geometry.”
So, your +2 level exams are over, and you are looking forward to join a college, but you do not really know which stream to choose. You, inevitably, have different people in your life, suggesting different streams to you, leaving you even more confused. While one stream brings you more money, the other one gives you a much stress-free life. Do not worry. Here is a guide through the tricky path. Following are some fine points of the streams available for graduation.
Arts or Humanities
If you are someone who has completed your schooling with an Arts background, you need to choose a course that suits your talent profile. It does not matter if you choose an academic course or a professional one; you need to be sure about your career goals. The stream of Arts offers you a wide array of courses which must be analysed properly before taking admission in any one of them. These courses include plain and simple B.A. or Bachelor of Arts, Hotel Management, Event Management, Fashion Designing, Mass Communication, and many more. All these courses offer lucrative career opportunities in the best industries worldwide. Besides, you can also go for Foreign Language Courses; these are high in demand, and help you get a job in multinational companies. The most frequently opted for foreign language courses are Spanish, French, Russian, Korean and Japanese.
Science
Science happens to offer the widest number of courses after 12th. If you have had a science background at school, your first two preferences would likely be Medicine and Engineering. Besides these, you can also opt for B.Sc degree in Physics, Chemistry, Biology or Mathematics; a degree in Agriculture, Forensic Science, Bio Technology, Geology, etc.
As Medicine and Engineering happen to be popular choices, we are going to elaborate on these two courses. If you choose Medicine, you can opt for any one of the following- Bachelor of Medicine and Bachelor of Surgery (MBBS), Bachelor of Physiotherapy, Bachelor of Ayurveda Medicine and Surgery (BAMS), Bachelor of Science in Optometry, Bachelor of Dental Surgery (BDS) and Bachelor of Pharmacy.
As far as Engineering is concerned, there is wide array of options, which include Aeronautical Engineering, Automobile Engineering, Civil Engineering, Electrical and Electronics Engineering, Computer and Communication Engineering, Information Technology Engineering, Mechanical Engineering, Chemical Engineering, Biomedical Engineering, etc.
Commerce
In case you are a Commerce student, it is quite likely that ‘Chartered Accountancy’ is what strikes your head. However, you need to begin with graduation. Courses such as BCom, BBA, BBS, BMS, etc., are some of the options Commerce students choose for their graduation. Besides, you can also opt for a diploma or certificate course in Taxation, Accounting, Applied Managerial Economics, Micro Finance, Banking and Insurance, Stock Market, Micro Finance, etc. Specialising in Commerce makes you eligible for jobs like that of Account Analyst, Account Assistant, Accounting Coordinator, Financial Consultant, Accounting Coordinator, Financial Auditor, Accounting Clerk, etc.
Think before you choose
There is no harm in taking others’ suggestions, but the ultimate decision must be yours. Nobody, but you know what you are comfortable at. It does not matter how much your parents coax you to take up Engineering, if you find Literature more interesting, go for it. After all, it is you who have to study the subject for the next three or four years, and build a future on the same. So, nobody but you can decide which course is best for you.
Also keep in mind that the course you choose gives you a good scope as far as career options are concerned. What you choose now will decide the shape of your future. So, please choose wisely.
Author’s bio: Jeff Traven is a professor at a well-known university is California. During his spare time, he likes to blog on various kinds topics that help young students choose the right courses after 12th, so that they can have a bright and prosperous future.
This is the real reason why exterior angles of a polygon add up to 360 degrees! If you shrink the polygon (which doesn’t affect the sum of exterior angles), the exterior angles eventually meet at a point, and the sum of angles at a point is 360 degrees.
Just to introduce a book that is based on an essay I wrote 10 years ago when I was a teenager. I decided to repackage it as a book published on Lulu.com:
Einstein, Relativity and Light for Kids: A book about Einstein, Relativity, and Light for Children. Includes an award-winning 2000 word Essay on “What happens if Light slows down”. Written when the author was 17 years old.
What happens if light slows down – A Beginner’s Guide to Relativity and Light
In the beginning God created the heavens and the earth. And God said, “Let there be light,” and there was light. Light is one of the most ubiquitous things that we see, and it is also one of the oldest – it existed since the beginning of mankind. However, light is also mysterious in that no one really understands what it is and how it is rectilinearly propagated. Nevertheless, the speed of light plays an important part in physics, and it is one of the more often quoted constant. What will happen then, if the speed of light suddenly changes from 300000000m/s to a fraction of its original self –3000 m/s? (It is theoretically possible to slow down light to such a speed, by shining a beam of light through a medium with a refractive index of 100,000.)
Hope this book will be useful to anyone trying to learn more about Einstein through a novel way! What will happen when light slows down? Read the book to find out! 🙂
This is a really beautiful Map of Mathematics (Mathematistan, a pun on Mathematics and Afghanistan), where one can see all the various branches of Maths, and how they combine together.
I also learnt a new word: Califate, which means an Islamic state led by a supreme religious and political leader known as a caliph – i.e. “successor” – to Muhammad.
Published Nov 25, 2003 by Addison-Wesley Professional. Part of the Tools and Techniques for Computer Typesetting series. The series editor may be contacted at frank.mittelbach@latex-project.org. LaTeX is the text-preparation system of choice for scientists and academics, and is especially useful for typesetting technical materials. This popular book shows you how to begin using LaTeX to create high-quality documents. The book also serves as a handy reference for all LaTeX users. In this completely revised edition, the authors cover the LaTeX2ε standard and offer more details, examples, exercises, tips, and tricks. They go beyond the core installation to describe the key contributed packages that have become essential to LaTeX processing.
Inside, you will find:
Complete coverage of LaTeX fundamentals, including how to input text, symbols, and mathematics; how to produce lists and tables; how to include graphics and color; and how to organize and customize documents
Discussion of more advanced concepts such as bibliographical databases and BIBTeX, math extensions with AMS-LaTeX, drawing, slides, and letters
Helpful appendices on installation, error messages, creating packages, using LaTeX with HTML and XML, and fonts
An extensive alphabetized listing of commands and their uses
New to this edition:
More emphasis on LaTeX as a markup language that separates content and form–consistent with the essence of XML
Detailed discussions of contributed packages alongside relevant standard topics
In-depth information on PDF output, including extensive coverage of how to use the hyperref package to create links, bookmarks, and active buttons
As did the three best-selling editions that preceded it, Guide to LaTeX, Fourth Edition,will prove indispensable to anyone wishing to gain the benefits of LaTeX.
The accompanying CD-ROM is part of the TeX Live set distributed by TeX Users Groups, containing a full LaTeX installation for Windows, MacOSX, and Linux, as well as many extensions, including those discussed in the book.
This revolutionary book establishes new foundations for trigonometry and Euclidean geometry. It shows how to replace transcendental trig functions with high school arithmetic and algebra to dramatically simplify the subject, increase accuracy in practical problems, and allow metrical geometry to be systematically developed over a general field. This new theory brings together geometry, algebra and number theory and sets out new directions for algebraic geometry, combinatorics, special functions and computer graphics. The treatment is careful and precise, with over one hundred theorems and 170 diagrams, and is meant for a mathematically mature audience. Gifted high school students will find most of the material accessible, although a few chapters require calculus. Applications include surveying and engineering problems, Platonic solids, spherical and cylindrical coordinate systems, and selected physics problems, such as projectile motion and Snell’s law. Examples over finite fields are also included.
What if you had to take an art class in which you were only taught how to paint a fence? What if you were never shown the paintings of van Gogh and Picasso, weren’t even told they existed? Alas, this is how math is taught, and so for most of us it becomes the intellectual equivalent of watching paint dry.
In Love and Math, renowned mathematician Edward Frenkel reveals a side of math we’ve never seen, suffused with all the beauty and elegance of a work of art. In this heartfelt and passionate book, Frenkel shows that mathematics, far from occupying a specialist niche, goes to the heart of all matter, uniting us across cultures, time, and space.
Love and Math tells two intertwined stories: of the wonders of mathematics and of one young man’s journey learning and living it. Having braved a discriminatory educational system to become one of the twenty-first century’s leading mathematicians, Frenkel now works on one of the biggest ideas to come out of math in the last 50 years: the Langlands Program. Considered by many to be a Grand Unified Theory of mathematics, the Langlands Program enables researchers to translate findings from one field to another so that they can solve problems, such as Fermat’s last theorem, that had seemed intractable before.
At its core, Love and Math is a story about accessing a new way of thinking, which can enrich our lives and empower us to better understand the world and our place in it. It is an invitation to discover the magic hidden universe of mathematics.
Now, I want you to imagine for a moment that you live in the United States, to be exact: New Hampshire. You’re a recruiter at the University of New Hampshireand your job is to hire the best people to become professors and lecturers.
Now suppose one day you get an application from this guy, Zhang Yitang, a 50-something mathematician. Since getting his PhD from Purdue, he’s struggled to find an academic job, working as a motel clerk and a Subway sandwich maker. I wouldn’t blame you if you passed over him.
It turns out if you had skipped Zhang Yitang, you’d have been making a big mistake, because a few weeks ago this 57-year old Chinese mathematician made headlines aroundtheworld when he proved a result in number theory which has been challenging mathematicians for years.
The Freakonomics of math—a math-world superstar unveils the hidden beauty and logic of the world and puts its power in our hands
The math we learn in school can seem like a dull set of rules, laid down by the ancients and not to be questioned. In How Not to Be Wrong, Jordan Ellenberg shows us how terribly limiting this view is: Math isn’t confined to abstract incidents that never occur in real life, but rather touches everything we do–the whole world is shot through with it.
Math allows us to see the hidden structures underneath the messy and chaotic surface of our world. It’s a science of not being wrong, hammered out by centuries of hard work and argument. Armed with the tools of mathematics, we can see through to the true meaning of information we take for granted: How early should you get to the airport? What does “public opinion” really represent? Why do tall parents have shorter children? Who really won Florida in 2000? And how likely are you, really, to develop cancer?
How Not to Be Wrong presents the surprising revelations behind all of these questions and many more, using the mathematician’s method of analyzing life and exposing the hard-won insights of the academic community to the layman–minus the jargon. Ellenberg chases mathematical threads through a vast range of time and space, from the everyday to the cosmic, encountering, among other things, baseball, Reaganomics, daring lottery schemes, Voltaire, the replicability crisis in psychology, Italian Renaissance painting, artificial languages, the development of non-Euclidean geometry, the coming obesity apocalypse, Antonin Scalia’s views on crime and punishment, the psychology of slime molds, what Facebook can and can’t figure out about you, and the existence of God.
Ellenberg pulls from history as well as from the latest theoretical developments to provide those not trained in math with the knowledge they need. Math, as Ellenberg says, is “an atomic-powered prosthesis that you attach to your common sense, vastly multiplying its reach and strength.” With the tools of mathematics in hand, you can understand the world in a deeper, more meaningful way. How Not to Be Wrong will show you how.
Need help with Geometry? Designed to replicate the services of a skilled private tutor, the new and improved Tutor in a Book’s Geometry is at your service! TIB’s Geometry is an extremely thorough, teen tested and effective geometry tutorial.
TIB’s Geometry includes more than 500 of the right, well-illustrated, carefully worked out and explained proofs and problems. Throughout TIB’s Geometry, there is ongoing, specific guidance as to the most effective solution and test taking strategies. Recurring patterns, which provide solutions to proofs, are pointed out, explained and illustrated using the visual aids that students find so helpful. Also included are dozens of graphic organizers, which help students understand, remember and recognize the connections between concepts.
TIB’s author Jo Greig intended this book to level the playing field between the students who have tutors and those that don’t. As a long time, very successful private mathematics tutor and teacher, Jo Greig knew exactly how best to accomplish this! TIB’s Geometry 294 pages are packed with every explanation, drawing, hint and memory tool possible! Not only does it have examples of the right proofs and problems, it also manages to impart every bit of the enthusiasm that great tutors impart to their private tutoring students. Ms. Greig holds a bachelors’ degree in mathematics. Dr. J. Shiletto, the book’s mathematics editor, holds a Ph.D in mathematics.
A reader of our Mathtuition88.com blog asked the following Maths question:
Given that and , where , express in terms of .
This is a rather challenging question, since there are many options to start. Which formula(s) should we use? Factor formula? R-formula? Give it a try first if you want to have a challenge.
Tough Test Questions? Missed Lectures? Not Enough Time?
Fortunately, there’s Schaum’s. This all-in-one-package includes more than 600 fully solved problems, examples, and practice exercises to sharpen your problem-solving skills. Plus, you will have access to 20 detailed videos featuring Math instructors who explain how to solve the most commonly tested problems–it’s just like having your own virtual tutor! You’ll find everything you need to build confidence, skills, and knowledge for the highest score possible.
More than 40 million students have trusted Schaum’s to help them succeed in the classroom and on exams. Schaum’s is the key to faster learning and higher grades in every subject. Each Outline presents all the essential course information in an easy-to-follow, topic-by-topic format. You also get hundreds of examples, solved problems, and practice exercises to test your skills.
This Schaum’s Outline gives you
618 fully solved problems to reinforce knowledge
Concise explanations of all trigonometry concepts
Updates that reflect the latest course scope and sequences, with coverage of periodic functions and curve graphing.
Fully compatible with your classroom text, Schaum’s highlights all the important facts you need to know. Use Schaum’s to shorten your study time–and get your best test scores!
As an Amazon Affiliate, Mathtuition88 is proud to introduce the Fire HD Kids Edition:
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Don’t worry about the bill—The Kids Edition includes a year of Amazon FreeTime Unlimited so kids get unlimited access to 5,000 books, movies, TV shows, educational apps, and games—at no additional cost.
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Kid-Proof Case—Durable, lightweight case to protect against drops and bumps caused by kids at play.
This is a potential good alternative to the Ipad. Ipad is more for games, while the Fire HD Kids Edition Tablet is more educational, with a hand-curated subscription of over 5,000 kid-friendly books, movies, TV shows, educational apps, and games.
It will be out soon this October 2014! Pre-order now by clicking this link: Click here to Pre-order.
What are Friedman numbers? Watch this video to find out!
Most amazing thing is that as numbers get bigger, the likelihood that they are Friedman numbers actually increase! (Friedman numbers have “density one”!)
Any high school student preparing for the American Mathematics Competitions should get their hands on a copy of this book! A major aspect of mathematical training and its benefit to society is the ability to use logic to solve problems. The American Mathematics Competitions (AMC) have been given for more than fifty years to millions of high school students. This book considers the basic ideas behind the solutions to the majority of these problems, and presents examples and exercises from past exams to illustrate the concepts. Anyone taking the AMC exams or helping students prepare for them will find many useful ideas here. But people generally interested in logical problem solving should also find the problems and their solutions interesting. This book will promote interest in mathematics by providing students with the tools to attack problems that occur on mathematical problem-solving exams, and specifically to level the playing field for those who do not have access to the enrichment programs that are common at the top academic high schools. The book can be used either for self-study or to give people who want to help students prepare for mathematics exams easy access to topic-oriented material and samples of problems based on that material. This is useful for teachers who want to hold special sessions for students, but it is equally valuable for parents who have children with mathematical interest and ability. As students’ problem solving abilities improve, they will be able to comprehend more difficult concepts requiring greater mathematical ingenuity. They will be taking their first steps towards becoming math Olympians!
I will now be receiving submissions for Carnival 115.
Firstly, let’s have a discussion on what is so special about the number 115. David Brooks has kindly provided a PDF (Input for Carnival of Math) which the following information is sourced from.
115 has a unique representation as a sum of three squares: 32 + 52 + 92 = 115.
115 is the smallest three-digit integer, abc, such that (abc)/(a*b*c) is prime: 115/5 = 23.
STS-115 was a space shuttle mission to the International Space Station flown by the space shuttle Atlantis on Sept. 9, 2006.
Some other interesting Trivia about 115 include:
115 is the emergency telephone number when calling in Iran. 🙂
115 is the number of cardinals who actually participated to vote for the 265th Pope succeeding the Pope John Paul II in April 2005, even though 117 cardinals were eligible.
This is a very interesting link about tetrominoes! If you are not sure what are tetrominoes, it is perfectly ok! Just go to the website link above and you will find out!
Question:How many different colored tetrominoes are there if we allow only four colors total?
Second question: What the heck is a tetromino?
Dominoes are a great game with rectangle tiles, composed of two adjacent squares with certain numbers of pips on them. A tetromino is a group of four adjacent squares, each sharing at least one side with at least one other square. In other words, those little falling shapes made popular in the game Tetris, and all of its knock-off variations, as seen below:
Summary: The use of the term ‘expected frequencies’ is novel and not widely known in mathematics education. The basic idea is very simple: instead of saying “the probability of X is 0.20 (or 20%)”, we would say “out of 100 situations like this, we would expect X to occur 20 times”.
Sigmund Freud tells the tale of a man accused of breaking his neighbour’s kettle. He mounts a three-stranded defence :
1. “I never borrowed it in the first place!”
2. “And anyway it was already broken when I did!”
3. “In any case, it was fine when I returned it!”
Freud used this as an example of the inconsistent logic of dreamland, although you won’t have to look too far afield in the waking world to find examples of similar reasoning[1].
From Math Circle: The reason I picked billiards to feature at this particular moment is because twoof this year’s Fields Medalists study billiards: Maryam Mirzakhani and Artur Avila. To find out more about these amazing mathematicians, see our recent Math Munch post.
The curious reluctance to define prime probability logically. The title says it all, except stress the point that we need to encourage more reasoning from first principles based on what we individually accept as self-evident, and not on what others believe to be self-evident.
By JoAnne Growney: One of my favorite mathy poets is Halifax mathematician Robert Dawson — his work is complex and inventive, and fun to puzzle over. Dawson’s webpage at St Mary’s University lists his mathematical activity; his poetry and fiction are available in several issues of the Journal of Humanistic Mathematics and in several postings for this blog (15 April 2012, 30 November 2013, 2 March 2014) and in various other locations findable by Google.
Can a poem be written by following a formula? Despite the tendency of most of us to say NO to this question we also may admit to the fact that a formula applied to words can lead to arrangements and thoughts not possible for us who write from our own learning and experiences. How else to be REALLY NEW but to try a new method? Set a chimpanzee at a typewriter or apply a mathematical formula.
Below we offer Dawson’s “Hailstone” and follow it with his explanation of how mathematics shaped the poem from its origin as a “found passage” from the beginning of Dickens’ Great Expectations.
Read this article to learn how to approximate e using just the digitis 1-9! ((1 + 9^{–4^{7×6}})^{3^{2^{85}}}. ) Learn how it works and how remarkably accurate it is! The post is written by Richard Green.
I was in one of my colleagues lessons this week.and he was teaching the class to expand quadratic brackets. As the lesson went on he noticed that a number of pupils had been writing the X squared term, then the constant term then the X term so he pulled the class together to tell them that conventionally we write quadratic equations in decending powers of x. This is excellent practice and something we all should be encouraging, but it made me think “Why decending powers of x?”
Interesting question to ponder!
Read more at: http://cavmaths.wordpress.com/2014/09/26/decending-powers-of-x/
From a well-known actress, math genius and popular contestant on “Dancing With The Stars”—a groundbreaking guide to mathematics for middle school girls, their parents, and educators
From a well-known actress, math genius and popular contestant on “Dancing With The Stars”—a groundbreaking guide to mathematics for middle school girls, their parents, and educators
As the math education crisis in this country continues to make headlines, research continues to prove that it is in middle school when math scores begin to drop—especially for girls—in large part due to the relentless social conditioning that tells girls they “can’t do” math, and that math is “uncool.” Young girls today need strong female role models to embrace the idea that it’s okay to be smart—in fact, it’s sexy to be smart!
It’s Danica McKellar’s mission to be this role model, and demonstrate on a large scale that math doesn’t suck. In this fun and accessible guide, McKellar—dubbed a “math superstar” by The New York Times—gives girls and their parents the tools they need to master the math concepts that confuse middle-schoolers most, including fractions, percentages, pre-algebra, and more. The book features hip, real-world examples, step-by-step instruction, and engaging stories of Danica’s own childhood struggles in math (and stardom). In addition, borrowing from the style of today’s teen magazines, it even includes a Math Horoscope section, Math Personality Quizzes, and Real-Life Testimonials—ultimately revealing why math is easier and cooler than readers think.
This book is intended for the Mathematical Olympiad students who wish to prepare for the study of inequalities, a topic now of frequent use at various levels of mathematical competitions. In this volume we present both classic inequalities and the more useful inequalities for confronting and solving optimization problems. An important part of this book deals with geometric inequalities and this fact makes a big difference with respect to most of the books that deal with this topic in the mathematical olympiad. The book has been organized in four chapters which have each of them a different character. Chapter 1 is dedicated to present basic inequalities. Most of them are numerical inequalities generally lacking any geometric meaning. However, where it is possible to provide a geometric interpretation, we include it as we go along. We emphasize the importance of some of these inequalities, such as the inequality between the arithmetic mean and the geometric mean, the Cauchy-Schwarz inequality, the rearrangementinequality, the Jensen inequality, the Muirhead theorem, among others. For all these, besides giving the proof, we present several examples that show how to use them in mathematical olympiad problems. We also emphasize how the substitution strategy is used to deduce several inequalities.
A small psychological change to how we approach challenges can drastically change how successful we are at these tasks.
That’s according to Carol Dweck, a psychology professor at Stanford University, who coined the term “growth mindset” in her 2007 book “Mindset: The New Psychology of Success.”
Microsoft magnate Bill Gates tweeted a video of Dweck explaining the growth mindset earlier this week:
World-renowned Stanford University psychologist Carol Dweck, in decades of research on achievement and success, has discovered a truly groundbreaking idea–the power of our mindset.
Dweck explains why it’s not just our abilities and talent that bring us success–but whether we approach them with a fixed or growth mindset. She makes clear why praising intelligence and ability doesn’t foster self-esteem and lead to accomplishment, but may actually jeopardize success. With the right mindset, we can motivate our kids and help them to raise their grades, as well as reach our own goals–personal and professional. Dweck reveals what all great parents, teachers, CEOs, and athletes already know: how a simple idea about the brain can create a love of learning and a resilience that is the basis of great accomplishment in every area.
Whether you are a student struggling to fulfill a math or science requirement, or you are embarking on a career change that requires a higher level of math competency, A Mind for Numbers offers the tools you need to get a better grasp of that intimidating but inescapable field. Engineering professor Barbara Oakley knows firsthand how it feels to struggle with math. She flunked her way through high school math and science courses, before enlisting in the army immediately after graduation. When she saw how her lack of mathematical and technical savvy severely limited her options—both to rise in the military and to explore other careers—she returned to school with a newfound determination to re-tool her brain to master the very subjects that had given her so much trouble throughout her entire life.
In A Mind for Numbers, Dr. Oakley lets us in on the secrets to effectively learning math and science—secrets that even dedicated and successful students wish they’d known earlier. Contrary to popular belief, math requires creative, as well as analytical, thinking. Most people think that there’s only one way to do a problem, when in actuality, there are often a number of different solutions—you just need the creativity to see them. For example, there are more than three hundred different known proofs of the Pythagorean Theorem. In short, studying a problem in a laser-focused way until you reach a solution is not an effective way to learn math. Rather, it involves taking the time to step away from a problem and allow the more relaxed and creative part of the brain to take over. A Mind for Numbers shows us that we all have what it takes to excel in math, and learning it is not as painful as some might think!
Whether you are a student struggling to fulfill a math or science requirement, or you are embarking on a career change that requires a higher level of math competency, A Mind for Numbers offers the tools you need to get a better grasp of that intimidating but inescapable field. Engineering professor Barbara Oakley knows firsthand how it feels to struggle with math. She flunked her way through high school math and science courses, before enlisting in the army immediately after graduation. When she saw how her lack of mathematical and technical savvy severely limited her options—both to rise in the military and to explore other careers—she returned to school with a newfound determination to re-tool her brain to master the very subjects that had given her so much trouble throughout her entire life.
In A Mind for Numbers, Dr. Oakley lets us in on the secrets to effectively learning math and science—secrets that even dedicated and successful students wish they’d known earlier. Contrary to popular belief, math requires creative, as well as analytical, thinking. Most people think that there’s only one way to do a problem, when in actuality, there are often a number of different solutions—you just need the creativity to see them. For example, there are more than three hundred different known proofs of the Pythagorean Theorem. In short, studying a problem in a laser-focused way until you reach a solution is not an effective way to learn math. Rather, it involves taking the time to step away from a problem and allow the more relaxed and creative part of the brain to take over. A Mind for Numbers shows us that we all have what it takes to excel in math, and learning it is not as painful as some might think!
There is an interesting upcoming course at Coursera, suitable for undergraduates! (Starting 12 September 2014) Join the class if interested, it is free! Functional Analysis is actually a third year course for Math Majors at university. There are some powerful and deep theorems in functional analysis, like the Riesz representation theorem.
About the Course
Functional analysis is the branch of mathematics dealing with spaces of functions. It is a valuable tool in theoretical mathematics as well as engineering. It is at the very core of numerical simulation.
In this class, I will explain the concepts of convergence and talk about topology. You will understand the difference between strong convergence and weak convergence. You will also see how these two concepts can be used.
You will learn about different types of spaces including metric spaces, Banach Spaces, Hilbert Spaces and what property can be expected. You will see beautiful lemmas and theorems such as Riesz and Lax-Milgram and I will also describe Lp spaces, Sobolev spaces and provide a few details about PDEs, or Partial Differential Equations.
Course Syllabus
Week 1: Topology; continuity and convergence of a sequence in a topological space.
Week 2: Metric and normed spaces; completeness
Week 3: Banach spaces; linear continuous functions; weak topology
Week 4: Hilbert spaces; The Riesz representation theorem
Week 5: The Lax-Milgram Lemma
Week 6: Properties of the Lp spaces
Week 7: Distributions and Sobolev Spaces
Week 8: Application: simulating a membrane
Recommended Background
The course is mostly self-contained; however, you need to be familiar with functions, derivatives and integrals. You need to know what A ∩ B means and to know what a proof is. You should be fine if you have taken Calculus II and Algebra II. Students in Europe who have taken 120 ECTS in science should be fine as well.
Because this is an online class, having advanced and non-advanced students in a class will not be a problem; on the contrary we expect a wide range of interesting interactions. However, non-advanced students may have to work a bit more.
Course Format
The class will consist of a series of lecture videos, usually between five and twelve minutes in length. There will be approximately one hour worth of video content per week. Some of the videos contain integrated quiz questions. There will also be standalone quizzes that are not part of the video lectures; you will be asked to solve some problems and evaluate the solutions proposed by your fellow classmates. There will be a final exam.
There will be some additional contents in the form of PDF files.
FAQ
Will I get a Statement of Accomplishment after completing this class?
Yes. Students who successfully complete the class will receive a Statement of Accomplishment signed by the instructor.
What resources will I need for this class?
For this course, all you need is an Internet connection and the time to view the videos, understand the material, discuss the material with fellow classmates, take the quizzes and solve the problems.
What pedagogy will be used?
This MOOC is in English but the math will be taught with a “French Touch”.
What does “teaching math with a French touch” mean?
France has a long-standing tradition where math is addressed from a theoretical standpoint and studied for its implicit value throughout high school and preparatory school for the high-level entrance exams. This leads to a mindset based on proofs and abstraction. This mindset has consequences on problem solving that is sometimes referred to as the “French Engineer”. In contrast, other countries have a tradition where math is addressed as a computation tool.
Does it mean it will abstract and complicated?
The approach will be rather abstract but I will be sure to emphasize the concepts over the technicalities. Above all, my aim is to help you understand the material and the beauty behind it.
Whether you are a student struggling to fulfill a math or science requirement, or you are embarking on a career change that requires a higher level of math competency, A Mind for Numbers offers the tools you need to get a better grasp of that intimidating but inescapable field. Engineering professor Barbara Oakley knows firsthand how it feels to struggle with math. She flunked her way through high school math and science courses, before enlisting in the army immediately after graduation. When she saw how her lack of mathematical and technical savvy severely limited her options—both to rise in the military and to explore other careers—she returned to school with a newfound determination to re-tool her brain to master the very subjects that had given her so much trouble throughout her entire life.
In A Mind for Numbers, Dr. Oakley lets us in on the secrets to effectively learning math and science—secrets that even dedicated and successful students wish they’d known earlier. Contrary to popular belief, math requires creative, as well as analytical, thinking. Most people think that there’s only one way to do a problem, when in actuality, there are often a number of different solutions—you just need the creativity to see them. For example, there are more than three hundred different known proofs of the Pythagorean Theorem. In short, studying a problem in a laser-focused way until you reach a solution is not an effective way to learn math. Rather, it involves taking the time to step away from a problem and allow the more relaxed and creative part of the brain to take over. A Mind for Numbers shows us that we all have what it takes to excel in math, and learning it is not as painful as some might think!
Whether you are a student struggling to fulfill a math or science requirement, or you are embarking on a career change that requires a higher level of math competency, A Mind for Numbers offers the tools you need to get a better grasp of that intimidating but inescapable field. Engineering professor Barbara Oakley knows firsthand how it feels to struggle with math. She flunked her way through high school math and science courses, before enlisting in the army immediately after graduation. When she saw how her lack of mathematical and technical savvy severely limited her options—both to rise in the military and to explore other careers—she returned to school with a newfound determination to re-tool her brain to master the very subjects that had given her so much trouble throughout her entire life.
In A Mind for Numbers, Dr. Oakley lets us in on the secrets to effectively learning math and science—secrets that even dedicated and successful students wish they’d known earlier. Contrary to popular belief, math requires creative, as well as analytical, thinking. Most people think that there’s only one way to do a problem, when in actuality, there are often a number of different solutions—you just need the creativity to see them. For example, there are more than three hundred different known proofs of the Pythagorean Theorem. In short, studying a problem in a laser-focused way until you reach a solution is not an effective way to learn math. Rather, it involves taking the time to step away from a problem and allow the more relaxed and creative part of the brain to take over. A Mind for Numbers shows us that we all have what it takes to excel in math, and learning it is not as painful as some might think!
Math + Comics = Learning That’s Fun! Help students build essential math skills and meet math standards with 80 laugh-out-loud comic strips and companion mini-story problems. Each reproducible comic and problem set reinforces a key math skill: multiplication, division, fractions, decimals, measurement, geometry, and more. Great to use for small-group or independent class work and for homework! For use with Grades 3-6.
Who says math can’t be funny? In Math Jokes 4 Mathy Folks, Patrick Vennebush dispels the myth of the humorless mathematician. His quick wit comes through in this incredible compilation of jokes and stories. Intended for all math types, Math Jokes 4 Mathy Folks provides a comprehensive collection of math humor, containing over 400 jokes. It’s a book that all teachers from elementary school through college should have in their library. But the humor isn’t just for the classroom-it also appeals to engineers, statisticians, and other math professionals searching for some good, clean, numerical fun. From basic facts (Why is 6 afraid of 7?) to trigonometry (Mathematical puns are the first sine of dementia) and algebra (Graphing rational functions is a pain in the asymptote), no topic is safe. As Professor Jim Rubillo notes, Math Jokes 4 Math Folks is an absolute gem for anyone dedicated to seeing mathematical ideas through puns, double meanings, and blatant bad jokes. Such perspectives help to see concepts and ideas in different and creative ways.
Parents, students and teachers often argue, with little evidence, about whether U.S. high schools begin too early in the morning. In the past three years, however, scientific studies have piled up, and they all lead to the same conclusion: a later start time improves learning. And the later the start, the better.Biological research shows that circadian rhythms shift during the teen years, pushing boys and girls to stay up later at night and sleep later into the morning. The phase shift, driven by a change in melatonin in the brain, begins around age 13, gets stronger by ages 15 and 16, and peaks at ages 17, 18 or 19.
Does that affect learning? It does, according to Kyla Wahlstrom, director of the Center for Applied Research and Educational Improvement at the University of Minnesota. She published a large study in February that tracked more than 9,000 students in eight public high schools in Minnesota, Colorado and Wyoming. After one semester, when school began at 8:35 a.m. or later, grades earned in math, English, science and social studies typically rose a quarter step—for example, up halfway from B to B+.
Read more at: http://www.scientificamerican.com/article/school-starts-too-early/?&WT.mc_id=SA_WR_20140827
Featured book: Linear Algebra and Its Applications, 4th Edition
Linear algebra is relatively easy for students during the early stages of the course, when the material is presented in a familiar, concrete setting. But when abstract concepts are introduced, students often hit a brick wall. Instructors seem to agree that certain concepts (such as linear independence, spanning, subspace, vector space, and linear transformations), are not easily understood, and require time to assimilate. Since they are fundamental to the study of linear algebra, students’ understanding of these concepts is vital to their mastery of the subject. David Lay introduces these concepts early in a familiar, concrete Rnsetting, develops them gradually, and returns to them again and again throughout the text so that when discussed in the abstract, these concepts are more accessible.
Today, we discuss an interesting topic rarely taught in school: The rational parametrization of a unit circle. That is, how to find the x coordinates and y coordinates of a circle expressed as a rational function? The usual parametrization of a circle is (cos t, sin t).
We consider the straight line (l), passing through the point A(1,0) and the point (0,h).
The gradient of this line is .
The y-intercept of this line is .
Hence the equation of line l is .
We know the equation of the unit circle is .
By solving the two simultaneous equations (boxed), we get a quadratic formula:
Solving the above using the quadratic formula gives us .
Using , we get .
Hence, is a parametrization of the unit circle.
We can use this to generate Pythagorean triples! Simply choose a value of h, say, .
Then .
.
Substituting into , and multiplying by the denominator, we get the Pythagorean Triple . Interesting?
This revolutionary book establishes new foundations for trigonometry and Euclidean geometry. It shows how to replace transcendental trig functions with high school arithmetic and algebra to dramatically simplify the subject, increase accuracy in practical problems, and allow metrical geometry to be systematically developed over a general field. This new theory brings together geometry, algebra and number theory and sets out new directions for algebraic geometry, combinatorics, special functions and computer graphics. The treatment is careful and precise, with over one hundred theorems and 170 diagrams, and is meant for a mathematically mature audience. Gifted high school students will find most of the material accessible, although a few chapters require calculus. Applications include surveying and engineering problems, Platonic solids, spherical and cylindrical coordinate systems, and selected physics problems, such as projectile motion and Snell’s law. Examples over finite fields are also included.
Fix your wobbly table with just a small tweak – but why does this work?
Reddit discussion: http://www.reddit.com/r/BradyHaran/co…
Featuring Matthias Kreck from the University of Bonn.
This is a one-of-a-kind reference for anyone with a serious interest in mathematics. Edited by Timothy Gowers, a recipient of the Fields Medal, it presents nearly two hundred entries, written especially for this book by some of the world’s leading mathematicians, that introduce basic mathematical tools and vocabulary; trace the development of modern mathematics; explain essential terms and concepts; examine core ideas in major areas of mathematics; describe the achievements of scores of famous mathematicians; explore the impact of mathematics on other disciplines such as biology, finance, and music–and much, much more.
Unparalleled in its depth of coverage, The Princeton Companion to Mathematics surveys the most active and exciting branches of pure mathematics, providing the context and broad perspective that are vital at a time of increasing specialization in the field. Packed with information and presented in an accessible style, this is an indispensable resource for undergraduate and graduate students in mathematics as well as for researchers and scholars seeking to understand areas outside their specialties.
This small book demonstrates the evolution of certain areas of modern mathematics by examining the work of past winners of the Fields Medal, the “Nobel Prize” of mathematics. Foreword by Freeman Dyson.
I’d forgotten just how full the first day of an ICM is. First, you need to turn up early for the opening ceremony, so you end up sitting around for an hour and half or so before it even starts. Then there’s the ceremony itself, which lasts a couple of hours. Then in the afternoon you have talks about the four Fields Medallists and the Nevanlinna Prize winner, with virtually no breaks. Then after a massive ten minutes, the Nevanlinna Prize winner talks about his (in this case) own work, about which you have just heard, but in a bit more detail. That took us to 5:45pm. And just to round things off, Jim Simons is giving a public lecture at 8pm, which I suppose I could skip but I think I’m not going to. (The result is that most of this post will be written after it, but right…
Currently we are available to tutor private candidates on weekday mornings.
Contact our friendly tutor Mr Wu: email at mathtuition88@gmail.com
Ad hoc O Level Maths Tuition
Nowadays students are often so busy that regular weekly tuition may not be an option. (Due to stay back in school, extra lessons etc.)
We offer Ad hoc O Level Maths Tuition at our tuition centre at Bishan. Students can come for tuition when they need to ask questions or clarify concepts.
Fees will be charged per lesson; this will fit the students’ busy schedule perfectly.
This is a continuation of the series of Algebraic Topology videos. Previous post was AlgTop 0.
Professor Wildberger is an interesting speaker. He holds some unorthodox views, for instance he doesn’t believe in “real numbers” or “infinite sets”. Nevertheless, his videos are excellent and educational. Highly recommended to watch!
The basic topological objects, the line and the circle are viewed in a new light. This is the full first lecture of this beginner’s course in Algebraic Topology, given by N J Wildberger at UNSW. Here we begin to introduce basic one dimensional objects, namely the line and the circle. However each can appear in rather a remarkable variety of different ways.
This revolutionary book establishes new foundations for trigonometry and Euclidean geometry. It shows how to replace transcendental trig functions with high school arithmetic and algebra to dramatically simplify the subject, increase accuracy in practical problems, and allow metrical geometry to be systematically developed over a general field. This new theory brings together geometry, algebra and number theory and sets out new directions for algebraic geometry, combinatorics, special functions and computer graphics. The treatment is careful and precise, with over one hundred theorems and 170 diagrams, and is meant for a mathematically mature audience. Gifted high school students will find most of the material accessible, although a few chapters require calculus. Applications include surveying and engineering problems, Platonic solids, spherical and cylindrical coordinate systems, and selected physics problems, such as projectile motion and Snell’s law. Examples over finite fields are also included.
This is the Introductory lecture to a beginner’s course in Algebraic Topology given by N J Wildberger of the School of Mathematics and Statistics at UNSW in 2010.
This first lecture introduces some of the topics of the course and three problems.
If you are curious about how to make the interesting flap of paper (Problem 1), the solution can be found here. 🙂
This revolutionary book establishes new foundations for trigonometry and Euclidean geometry. It shows how to replace transcendental trig functions with high school arithmetic and algebra to dramatically simplify the subject, increase accuracy in practical problems, and allow metrical geometry to be systematically developed over a general field. This new theory brings together geometry, algebra and number theory and sets out new directions for algebraic geometry, combinatorics, special functions and computer graphics. The treatment is careful and precise, with over one hundred theorems and 170 diagrams, and is meant for a mathematically mature audience. Gifted high school students will find most of the material accessible, although a few chapters require calculus. Applications include surveying and engineering problems, Platonic solids, spherical and cylindrical coordinate systems, and selected physics problems, such as projectile motion and Snell’s law. Examples over finite fields are also included.
Secrets of Mental Math will have you thinking like a math genius in no time. Get ready to amaze your friends—and yourself—with incredible calculations you never thought you could master, as renowned “mathemagician” Arthur Benjamin shares his techniques for lightning-quick calculations and amazing number tricks. This book will teach you to do math in your head faster than you ever thought possible, dramatically improve your memory for numbers, and—maybe for the first time—make mathematics fun.
Yes, even you can learn to do seemingly complex equations in your head; all you need to learn are a few tricks. You’ll be able to quickly multiply and divide triple digits, compute with fractions, and determine squares, cubes, and roots without blinking an eye. No matter what your age or current math ability, Secrets of Mental Math will allow you to perform fantastic feats of the mind effortlessly. This is the math they never taught you in school.
Reviews:
“The clearest, simplest, most entertaining, and best book yet on the art of calculating in your head.” —Martin Gardner, author of Mathematical Magic Show and Mathematical Carnival
Check out this video of a Filipino street kid, who can calculate square roots without a calculator, and even knows the concepts of perfect squares and imaginary numbers!
Compare and contrast with this video:
No matter whether you are good or not so good at Math, it is never too late to learn! It is always possible to improve in Math.
Magical Mathematics reveals the secrets of amazing, fun-to-perform card tricks–and the profound mathematical ideas behind them–that will astound even the most accomplished magician. Persi Diaconis and Ron Graham provide easy, step-by-step instructions for each trick, explaining how to set up the effect and offering tips on what to say and do while performing it. Each card trick introduces a new mathematical idea, and varying the tricks in turn takes readers to the very threshold of today’s mathematical knowledge. For example, the Gilbreath Principle–a fantastic effect where the cards remain in control despite being shuffled–is found to share an intimate connection with the Mandelbrot set. Other card tricks link to the mathematical secrets of combinatorics, graph theory, number theory, topology, the Riemann hypothesis, and even Fermat’s last theorem.
Diaconis and Graham are mathematicians as well as skilled performers with decades of professional experience between them. In this book they share a wealth of conjuring lore, including some closely guarded secrets of legendary magicians. Magical Mathematics covers the mathematics of juggling and shows how the I Ching connects to the history of probability and magic tricks both old and new. It tells the stories–and reveals the best tricks–of the eccentric and brilliant inventors of mathematical magic.Magical Mathematics exposes old gambling secrets through the mathematics of shuffling cards, explains the classic street-gambling scam of three-card monte, traces the history of mathematical magic back to the thirteenth century and the oldest mathematical trick–and much more.
Clouds are not spheres, mountains are not cones, and lightening does not travel in a straight line. The complexity of nature’s shapes differs in kind, not merely degree, from that of the shapes of ordinary geometry, the geometry of fractal shapes.
Now that the field has expanded greatly with many active researchers, Mandelbrot presents the definitive overview of the origins of his ideas and their new applications. The Fractal Geometry of Nature is based on his highly acclaimed earlier work, but has much broader and deeper coverage and more extensive illustrations.
From search engines to big data and cloud services, math plays a key role in IT applications. Read on to know more about the opportunities math has to offer.
In this increasingly digital world, mathematics is everywhere. It is wise to keep track of the myriad opportunities that would be laid open by mathematics education.
“The advancement and perfection of mathematics are intimately connected with the prosperity of the state,” said Napolean Bonaparte. While there may be several opinions regarding Napolean as a leader, this statement holds indisputably true even today.
Read more at: http://www.thehindu.com/features/education/careers/stay-ahead-with-math/article6252546.ece
More than 80 or 90 per cent of students on four-year direct honours programmes at publicly-funded universities here graduate with honours or the equivalent. But only 60 per cent of those in the three-year arts and social sciences, business and science degree courses at the National University of Singapore (NUS) qualify for the fourth year of study, which allows them to graduate with honours.
To close the gap, NUS is lowering the grade to qualify for the honours year in these three schools, which are among the larger faculties in the university and take in some 3,600 students a year. This means another 10 to 15 per cent – 400 to 500 students- from these three faculties can move on to the fourth year to study for their honours.
Previously, students in the three faculties require a Cumulative Average Point (CAP) of 3.5 and above to qualify for honours study. With the change, they need only 3.2. NUS, though, will stick to its policy of keeping the the three plus one structure. Students who fail to notch up a score of at least 3.2 will have to exit the course.
NUS Provost Tan Eng Chye said the university decided to lower the requirement as the quality of students has gone up over the years. Students need As and Bs to enter most of the courses now. Last year, for example, students needed a ABB to enter the arts and social sciences course and those entering business needed triple As.
With more than five million copies in print all around the world, The 7 Habits of Highly Effective Teens is the ultimate teenage success guide—now updated for the digital age.
Imagine you had a roadmap—a step-by-step guide to help you get from where you are now, to where you want to be in the future. Your goals, your dreams, your plans…they are all within reach. You just need the tools to help you get there.
That’s what Sean Covey’s landmark book, The 7 Habits of Highly Effective Teens, has been to millions of teens: a handbook to self-esteem and success. Now updated for the digital age, this classic book applies the timeless principles of the 7 Habits to the tough issues and life-changing decisions teens face. In an entertaining style, Covey provides a simple approach to help teens improve self-image, build friendships, resist peer pressure, achieve their goals, and get along with their parents, as well as tackle the new challenges of our time, like cyberbullying and social media. In addition, this book is stuffed with cartoons, clever ideas, great quotes, and incredible stories about real teens from all over the world.
An indispensable book for teens, as well as parents, teachers, counselors, or any adult who works with teens, The 7 Habits of Highly Effective Teenshas become the last word on surviving and thriving as a teen and beyond.
“If The 7 Habits of Highly Effective Teens doesn’t help you, then you must have a perfect life already.”–Jordan McLaughlin, Age 17
Prodded by several comments, I have finally decided to write up some my thoughts on time management here. I actually have been drafting something about this subject for a while, but I soon realised that my own experience with time management is still very much a work in progress (you should see my backlog of papers that need writing up) and I don’t yet have a coherent or definitive philosophy on this topic (other than my advice on writing papers, for instance my page on rapid prototyping). Also, I can only talk about my own personal experiences, which probably do not generalise to all personality types or work situations, though perhaps readers may wish to contribute their own thoughts, experiences, or suggestions in the comments here. [I should also add that I don’t always follow my own advice on these matters, often to my own regret.]
Excellent and educational post by famous Mathematician Timothy Gowers on how to solve Math (Olympiad) problems.
(Post is at the bottom of this article)
Many students often give up immediately when facing a difficult maths problem. However, if students persist on for some time, usually they can come up with a solution or at least an idea on how to solve the problem. That is a great achievement already!
Never give up, even when your Maths question looks like this!
Quote: What I wrote gives some kind of illustration of the twists and turns, many of them fruitless, that people typically take when solving a problem. If I were to draw a moral from it, it would be this: when trying to solve a problem, it is a mistake to expect to take a direct route to the solution. Instead, one formulates subquestions and gradually builds up a useful bank of observations until the direct route becomes clear. Given that we’ve just had the football world cup, I’ll draw an analogy that I find not too bad (though not perfect either): a team plays better if it patiently builds up to an attack on goal than if it hoofs the ball up the pitch or takes shots from a distance. Germany gave an extraordinary illustration of this in their 7-1 defeat of Brazil.
This is a one-of-a-kind reference for anyone with a serious interest in mathematics. Edited by Timothy Gowers, a recipient of the Fields Medal, it presents nearly two hundred entries, written especially for this book by some of the world’s leading mathematicians, that introduce basic mathematical tools and vocabulary; trace the development of modern mathematics; explain essential terms and concepts; examine core ideas in major areas of mathematics; describe the achievements of scores of famous mathematicians; explore the impact of mathematics on other disciplines such as biology, finance, and music–and much, much more.
Unparalleled in its depth of coverage, The Princeton Companion to Mathematics surveys the most active and exciting branches of pure mathematics, providing the context and broad perspective that are vital at a time of increasing specialization in the field. Packed with information and presented in an accessible style, this is an indispensable resource for undergraduate and graduate students in mathematics as well as for researchers and scholars seeking to understand areas outside their specialties.
Features nearly 200 entries, organized thematically and written by an international team of distinguished contributors
Presents major ideas and branches of pure mathematics in a clear, accessible style
Defines and explains important mathematical concepts, methods, theorems, and open problems
Introduces the language of mathematics and the goals of mathematical research
Covers number theory, algebra, analysis, geometry, logic, probability, and more
Traces the history and development of modern mathematics
Profiles more than ninety-five mathematicians who influenced those working today
Explores the influence of mathematics on other disciplines
Includes bibliographies, cross-references, and a comprehensive index
Contributors incude:
Graham Allan, Noga Alon, George Andrews, Tom Archibald, Sir Michael Atiyah, David Aubin, Joan Bagaria, Keith Ball, June Barrow-Green, Alan Beardon, David D. Ben-Zvi, Vitaly Bergelson, Nicholas Bingham, Béla Bollobás, Henk Bos, Bodil Branner, Martin R. Bridson, John P. Burgess, Kevin Buzzard, Peter J. Cameron, Jean-Luc Chabert, Eugenia Cheng, Clifford C. Cocks, Alain Connes, Leo Corry, Wolfgang Coy, Tony Crilly, Serafina Cuomo, Mihalis Dafermos, Partha Dasgupta, Ingrid Daubechies, Joseph W. Dauben, John W. Dawson Jr., Francois de Gandt, Persi Diaconis, Jordan S. Ellenberg, Lawrence C. Evans, Florence Fasanelli, Anita Burdman Feferman, Solomon Feferman, Charles Fefferman, Della Fenster, José Ferreirós, David Fisher, Terry Gannon, A. Gardiner, Charles C. Gillispie, Oded Goldreich, Catherine Goldstein, Fernando Q. Gouvêa, Timothy Gowers, Andrew Granville, Ivor Grattan-Guinness, Jeremy Gray, Ben Green, Ian Grojnowski, Niccolò Guicciardini, Michael Harris, Ulf Hashagen, Nigel Higson, Andrew Hodges, F. E. A. Johnson, Mark Joshi, Kiran S. Kedlaya, Frank Kelly, Sergiu Klainerman, Jon Kleinberg, Israel Kleiner, Jacek Klinowski, Eberhard Knobloch, János Kollár, T. W. Körner, Michael Krivelevich, Peter D. Lax, Imre Leader, Jean-François Le Gall, W. B. R. Lickorish, Martin W. Liebeck, Jesper Lützen, Des MacHale, Alan L. Mackay, Shahn Majid, Lech Maligranda, David Marker, Jean Mawhin, Barry Mazur, Dusa McDuff, Colin McLarty, Bojan Mohar, Peter M. Neumann, Catherine Nolan, James Norris, Brian Osserman, Richard S. Palais, Marco Panza, Karen Hunger Parshall, Gabriel P. Paternain, Jeanne Peiffer, Carl Pomerance, Helmut Pulte, Bruce Reed, Michael C. Reed, Adrian Rice, Eleanor Robson, Igor Rodnianski, John Roe, Mark Ronan, Edward Sandifer, Tilman Sauer, Norbert Schappacher, Andrzej Schinzel, Erhard Scholz, Reinhard Siegmund-Schultze, Gordon Slade, David J. Spiegelhalter, Jacqueline Stedall, Arild Stubhaug, Madhu Sudan, Terence Tao, Jamie Tappenden, C. H. Taubes, Rüdiger Thiele, Burt Totaro, Lloyd N. Trefethen, Dirk van Dalen, Richard Weber, Dominic Welsh, Avi Wigderson, Herbert Wilf, David Wilkins, B. Yandell, Eric Zaslow, Doron Zeilberger
The title of this post is a nod to Terry Tao’s four mini-polymath discussions, in which IMO questions were solved collaboratively online. As the beginning of what I hope will be a long exercise in gathering data about how humans solve these kinds of problems, I decided to have a go at one of this year’s IMO problems, with the idea of writing down my thoughts as I went along. Because I was doing that (and doing it directly into a LaTeX file rather than using paper and pen), I took quite a long time to solve the problem: it was the first question, and therefore intended to be one of the easier ones, so in a competition one would hope to solve it quickly and move on to the more challenging questions 2 and 3 (particularly 3). You get an average of an hour and a half per…
Professor David Eisenbud gives an excellent explanation of the Fundamental Theorem of Algebra!
In high school, we learnt that some quadratic equations (e.g. ) do not have real roots. However, by the Fundamental Theorem of Algebra, every polynomial equation of degree d has d complex roots! (counting multiplicity)
Learn about the boy who – could read and add numbers when he was three years old, – thwarted his teacher by finding a quick and easy way to sum the numbers 1-100, – attracted the attention of a Duke with his genius, and became the man who… – predicted the reappearance of a lost planet, – discovered basic properties of magnetic forces, – invented a surveying tool used by professionals until the invention of lasers. Based on extensive research of original and secondary sources, this historical narrative will inspire young readers and even curious adults with its touching story of personal achievement.
Most students taking science related courses like Engineering or Physics need to study at least one semester of Calculus. Calculus can be a rather difficult subject, and having a good textbook to learn from is half the battle won! 🙂
We review 3 of the Top Calculus Textbooks on Amazon.com:
The Larson CALCULUS program has a long history of innovation in the calculus market. It has been widely praised by a generation of students and professors for its solid and effective pedagogy that addresses the needs of a broad range of teaching and learning styles and environments. Each title is just one component in a comprehensive calculus course program that carefully integrates and coordinates print, media, and technology products for successful teaching and learning.
This book by Michael Spivak is strongly recommended for Math Majors, or for students interested in learning the theory behind calculus. Includes the theory of epsilon-delta analysis.
3) Thomas’ Calculus (13th Edition)
Thomas’ Calculus, Thirteenth Edition, introduces readers to the intrinsic beauty of calculus and the power of its applications. For more than half a century, this text has been revered for its clear and precise explanations, thoughtfully chosen examples, superior figures, and time-tested exercise sets. With this new edition, the exercises were refined, updated, and expanded–always with the goal of developing technical competence while furthering readers’ appreciation of the subject. Co-authors Hass and Weir have made it their passion to improve the text in keeping with the shifts in both the preparation and ambitions of today’s learners.
This text is designed for a three-semester or four-quarter calculus course (math, engineering, and science majors).
and 
, where 
, express 
in terms of 
.
.
.
. Prove that
Wishing all teachers a happy Teacher’s Day this Friday, and also wishing students all the best for their upcoming exams.
.
.
.
.
.
.
is a parametrization of the unit circle.
.
.
.
. Interesting?
) do not have real roots. However, by the Fundamental Theorem of Algebra, every polynomial equation of degree d has d complex roots! (counting multiplicity)
Mathtuition88 