Motivational Books for the Student (Educational)

Christmas is almost here, and what could be a better Christmas present than a motivational book? Books, although viewed as old-fashioned in the current world of iPhones and iPads, are still very important learning tools that can change a person’s life.

Sometimes, bright or even gifted children don’t do well in school, because of motivational issues. Many academically weak students are actually bright students, but not focused on studies due to lack of motivation. They may feel that school is boring, or see school as a chore. Teenage years are often a difficult period of time. If successfully motivated, these children can often make a wondrous turnaround to get back on track academically.

Let me share some books that are actually purchased by viewers from my website through Amazon.com:

1) 
Chicken Soup for the Soul: Think Positive for Kids: 101 Stories about Good Decisions, Self-Esteem, and Positive Thinking

2) 
Drive: 9 Ways to Motivate Your Kids to Achieve

3) 
Empowering Underachievers: New Strategies to Guide Kids (8-18) to Personal Excellence

4) 
Have a New Kid by Friday: How to Change Your Child’s Attitude, Behavior & Character in 5 Days

5)
Making Children Mind without Losing Yours

6) 
Motivate Your Son: Inspire Your Boy To Be Engaged In School, Excited For College, and Energized For Success

7) 
Smart Parenting for Smart Kids: Nurturing Your Child’s True Potential

8)
The Motivation Breakthrough: 6 Secrets to Turning On the Tuned-Out Child

Inspirational Video by Nick Vujicic – DVD Clip from No Arms, No Legs, No Worries – Jr. High Talk


Life Without Limits: Inspiration for a Ridiculously Good Life

Chinese Tuition

Chinese Tuition coming soon

Chinese is becoming a very important language to learn, with China already overtaking the US to become the world’s largest economy, according to the International Monetary Fund.

Most importantly, Chinese is not just a language, it is a philosophy. Through learning the beauty of Chinese proverbs and idioms, one can gain the wisdom of the ancient Chinese sages and poets.

We will be partnering another teacher soon to offer Chinese Tuition!

Check out our main page at: Chinese Tuition Singapore


Featured book:

The Rise of China vs. the Logic of Strategy

As the rest of the world worries about what a future might look like under Chinese supremacy, Edward Luttwak worries about China’s own future prospects. Applying the logic of strategy for which he is well known, Luttwak argues that the most populous nation on Earth—and its second largest economy—may be headed for a fall.

For any country whose rising strength cannot go unnoticed, the universal logic of strategy allows only military or economic growth. But China is pursuing both goals simultaneously. Its military buildup and assertive foreign policy have already stirred up resistance among its neighbors, just three of whom—India, Japan, and Vietnam—together exceed China in population and wealth. Unless China’s leaders check their own ambitions, a host of countries, which are already forming tacit military coalitions, will start to impose economic restrictions as well.

Chinese leaders will find it difficult to choose between pursuing economic prosperity and increasing China’s military strength. Such a change would be hard to explain to public opinion. Moreover, Chinese leaders would have to end their reliance on ancient strategic texts such as Sun Tzu’s Art of War. While these guides might have helped in diplomatic and military conflicts within China itself, their tactics—such as deliberately provoking crises to force negotiations—turned China’s neighbors into foes. To avoid arousing the world’s enmity further, Luttwak advises, Chinese leaders would be wise to pursue a more sustainable course of economic growth combined with increasing military and diplomatic restraint.

254A announcement: Analytic prime number theory

Bookmark Terence Tao’s site if you are interested in his notes on Analytic number theory! He will be placing lecture notes online on his blog.
This is a one-in-a-lifetime chance to learn Analytic Number Theory from a Master — Fields Medallist Terence Tao.

Terence Tao's avatarWhat's new

In the winter quarter (starting January 5) I will be teaching a graduate topics course entitled “An introduction to analytic prime number theory“. As the name suggests, this is a course covering many of the analytic number theory techniques used to study the distribution of the prime numbers $latex {{mathcal P} = {2,3,5,7,11,dots}}&fg=000000$. I will list the topics I intend to cover in this course below the fold. As with my previous courses, I will place lecture notes online on my blog in advance of the physical lectures.

The type of results about primes that one aspires to prove here is well captured by Landau’s classical list of problems:

  1. Even Goldbach conjecture: every even number $latex {N}&fg=000000$ greater than two is expressible as the sum of two primes.
  2. Twin prime conjecture: there are infinitely many pairs $latex {n,n+2}&fg=000000$ which are simultaneously prime.
  3. Legendre’s conjecture:…

View original post 3,927 more words

Music and Mathematics are Apolitical

tomcircle's avatarMath Online Tom Circle

This “Butterfly Lovers Violin Concerto” (梁山伯与祝英台) composed 50 years ago by 2 Chinese music students, now played so lovely by a Japanese lady violinist. 

Only in the kingdom of Music (the other one is Mathematics) where human political hatred does not exist between countries due to past wars: Japan and China, Germany and the Allied Nations, … Just only yesterday China President Xi and Japan PM Abe both showed awkward “poker face” hand-shake at the APEC Beijing meeting; contrast to the 20th century’s greatest mathematician David Hilbert from Nazi Germany was welcome  in America to chair  the inauguration of the International Conference of Math.


If more students love Math and Music, the world of tomorrow will be more peaceful.

Watch 諏訪內晶子 -《梁祝小提琴協奏曲》   Butterfly Lovers Violin Concerto:

Notes:
1. The legendary love story is the Chinese version of “Romeo & Juliette”:

http://en.m.wikipedia.org/wiki/Butterfly_Lovers’_Violin_Concerto

2. On [13:27mins] the only single…

View original post 51 more words

数学大师: 无法

tomcircle's avatarMath Online Tom Circle

我现正在上2010全国华乐比赛-大师班。
大师音乐评分标准:
1. 大法(基本功)
2. 小法(特色)
3. 无法(风格)

数学大师Math Masters 也是如此,
1. 大法(基本功 Classical Math)
2. 小法(特色 Math Olympiad techniques)
3. 无法(风格 Abstract Math -> French “Math Composition“)

View original post

Funny Trigonometry Joke

Source: http://spikedmath.com/

Spiked Math Comic - Difference between sine and cosine

Get the joke? 🙂

Hint: Sine and Cosine differ by a phase difference of 90 degrees, since \sin(x+90^\circ)=\cos (x).


Featured book:

Trigonometry For Dummies

A plain-English guide to the basics of trig

Trigonometry deals with the relationship between the sides and angles of triangles… mostly right triangles. In practical use, trigonometry is a friend to astronomers who use triangulation to measure the distance between stars. Trig also has applications in fields as broad as financial analysis, music theory, biology, medical imaging, cryptology, game development, and seismology.

From sines and cosines to logarithms, conic sections, and polynomials, this friendly guide takes the torture out of trigonometry, explaining basic concepts in plain English and offering lots of easy-to-grasp example problems. It also explains the “why” of trigonometry, using real-world examples that illustrate the value of trigonometry in a variety of careers.

  • Tracks to a typical Trigonometry course at the high school or college level
  • Packed with example trig problems
  • From the author of Trigonometry Workbook For Dummies

Trigonometry For Dummies is for any student who needs an introduction to, or better understanding of, high-school to college-level trigonometry.

 

Leyland Numbers

Leyland Numbers – Numberphile

Check out this interesting video about Leyland Numbers, numbers of the form x^y+y^x, where x, y are larger than 1!

A curious and open question is: Which Leyland numbers happen to be prime?


Featured book:

Prime Obsession: Bernhard Riemann and the Greatest Unsolved Problem in Mathematics

In 1859, Bernhard Riemann, a little-known thirty-two year old mathematician, made a hypothesis while presenting a paper to the Berlin Academy titled  “On the Number of Prime Numbers Less Than a Given Quantity.”  Today, after 150 years of careful research and exhaustive study, the Riemann Hyphothesis remains unsolved, with a one-million-dollar prize earmarked for the first person to conquer it.

Alternating passages of extraordinarily lucid mathematical exposition with chapters of elegantly composed biography and history, Prime Obsession is a fascinating and fluent account of an epic mathematical mystery that continues to challenge and excite the world.

Rated 4.5/5 stars on Amazon!

Sums of kth powers

Very nice proof for the sum of kth powers. Recommended for reading!

gowers's avatarGowers's Weblog

Recently I was giving a talk at a school in London and had cause to think about sums of kth powers, because I wanted to show people the difference between unenlightening proofs and enlightening ones. (My brief was to try to give them some idea of what proofs are and why they are worth bothering about.) On the train down, I realized that there is a very simple general argument that can be used to work out formulae for sums of kth powers. After a brief look online, I haven’t found precisely this method, though I’ve found plenty of methods in the vicinity of it. It’s bound to be in the literature somewhere, so perhaps somebody can point me towards a reference. But even so, it’s worth a short post.

I’ll start with the case $latex k=1$. I want to phrase a familiar argument in a way that will make…

View original post 1,296 more words

What is Ideal ?

Ideal is used everywhere in Modern Math (Algebra, Topology, Quantum Group…)

tomcircle's avatarMath Online Tom Circle

Anything inside x outside still comes back inside

=> Zero x Anything = Zero

=> Even x Anything = Even

Mathematically,

1. nZ is an Ideal, represented by (n)

Eg. Even subring (2Z) x anything big Ring Z = 2Z = Even

2. (football) Field F is ‘sooo BIG’ that

(inside = outside)

=> Field has NO Ideal (except trivial 0 and F)

Why was Ideal invented ? because of ‘failure” of UNIQUE Primes Factorization” for this case (example):

6 = 2 x 3
but also
$latex 6=(1+sqrt{-5})(1-sqrt{-5})$
=> two factorizations !
=> violates the Fundamental Law of Arithmetic which says UNIQUE Prime Factorization

Unique Prime factors exist called Ideal Primes: $latex mbox{gcd = 2} , mbox{ 3}$, $latex (1+sqrt{-5})$, $latex (1-sqrt{-5}) $

Greatest Common Divisor (gcd or H.C.F.):
For n,m in Z
gcd (a,b)= ma+nb
Example: gcd(6,8) = (-1).6+(1).8=2
(m=-1, n=-1)

Dedekind’s Ideals (Ij):
6 =2×3= u.v =I1.I2.I3.I4…

View original post 112 more words

Recommended IB Math Books

The IB programme is gaining popularity throughout the world. In Singapore, some schools offer the IB Programme instead of the A Levels, most notably being ACS (International).

The IB Mathematics definitely has some interesting topics, including Number Theory, Graph Theory, and even Group Theory. These interesting topics are usually not learnt in JC.

Here are some Recommended IB Math Books from Amazon.com:

Most popular IB Math Books

1) 

IB Mathematics Standard Level (Oxford IB Diploma Programme)

2)

Barron’s IB Math SL

3)


IB Mathematics Higher Level Course Book: Oxford IB Diploma Program (International Baccalaureate)

4)

Workbook – IB Diploma Math SL part 1: This is a math workbook for students doing their IB diploma programme in math SL.

5)

Barron’s IB Math Studies

Best Rubik’s Cube (Cheap and Good) — The Dayan Zhanchi?

The Rubik’s Cube is a famous puzzle, that is related to Math and Group Theory. (See this free introduction by MIT on the The Mathematics of the Rubik’s Cube)

Recently, I am thinking of buying a new Rubik’s Cube, and searched on the internet on what is the best brand of Rubik’s Cube. For Rubik’s Cube, smoothness while turning is really important, because it will simply be easier to turn the edges if the cube is smooth.

After researching online, I came to a very surprising conclusion: The “made in China” brand Dayan Zhanchi is supposedly much better than the official Rubik’s brand (and also other “Western” brands)!


Dayan ® ZhanChi 3x3x3 Speed Cube 6-Color Stickerless

This amazing superhuman World Record is set using the Dayan Zhanchi! (2013, Mats Valk)

Other than the Dayan series, another alternative is the V-cube series:

V-CUBE 3 White Multicolor Cube

However, the reviews on Amazon seem to indicate that the Dayan is superior in both smoothness and price!

If you have any recommendations on which Rubik’s Cube is best, please write in the comments below!

I will be buying the Dayan Cube soon (hopefully in time for Christmas 2014), and will post new updates! I am most probably buying the stickerless version since I have past experience of stickers falling off from my previous cubes. (Note: Stickerless Rubik’s Cubes are banned from competitions for the ridiculous reason that it is possible to “see what colors are behind through the cracks”, see https://github.com/cubing/wca-documents/issues/177) So if your goal is to enter a competition, you may want to consider the sticker version of the Zhanchi.

For parents, buying a Rubik’s cube for your child is a great investment. Playing with the Rubik’s cube is a major intellectual challenge (it has 43 quintillion permutations, only 1 of which is correct), which will develop the child’s brain for logical thinking, which is especially useful for Math and Science. Most importantly, it is fun!


Dayan ® ZhanChi 3x3x3 Speed Cube 6-Color Stickerless

Special note for buying Dayan Zhanchi from Singapore:

If you are buying the Dayan Zhanchi from Singapore, at first it seems like the Dayan ZhanChi does not ship to Singapore. It actually does! We just have to choose the correct seller, Cube Puzl, which ships to Singapore.

other sellers

cube puzl

Looking for a reliable Tuition Agency?

Looking for a reliable Tuition Agency?

Its the holiday period now, and many parents are looking to find a tutor for the next academic year. Please look no further, as Startutor is the best tuition agency in Singapore, winning hands down. I have worked with Startutor both as a tutor and an affiliate, and am impressed by their professional website (one of the best website designs around), and their professional attitude.

For other subjects besides Mathematics, request for a tutor at Startutor! Startutor is Singapore’s most popular online agency, providing tutors to your home. There are no extra costs for making a request. Tutors’ certificates are carefully vetted by Startutor. (Website: http://startutor.sg/request,wwcsmt)

Startutor is suitable for English Tuition, Social Studies Tuition, Geography Tuition, Physics Tuition, Chemistry Tuition, Biology Tuition, Chinese Tuition,Economics Tuition, GP Tuition, Piano Lessons and more!

Startutor: http://startutor.sg/request,wwcsmt

(Please use the full link above directly, thanks!)

Screenshot:

startutor screenshot

Top 20 World’s Best Universities

tomcircle's avatarMath Online Tom Circle

http://finance.yahoo.com/news/harvard-tops-us-news-world-150403455.html

These 20 are purely anglophone universities — USA (16), UK(3), Canada (1).

The report is too biased. I am sure there are some non-anglophone universities in Europe, Australia and Asia which are equally good, if not better, than some of those in this list.

image

image

View original post

Self-study Advanced Math

tomcircle's avatarMath Online Tom Circle

I came across this review at Amazon in 2007 on how to study Advanced Math on your own. Wonderful advice !

Give yourself 10-15 years, with passion, interest, dedicated commitment, disciplined, you could self-study Math to be a next Fermat, or Hua Luogen – both learned Math by themselves through self-learning from books.

http://www.amazon.com/gp/richpub/syltguides/fullview/R1GE1P236K3YSV/ref=cm_syt_dtpa_f_1_rdssss1/102-4263436-5550568?pf_rd_m=ATVPDKIKX0DER&pf_rd_s=sylt-center&pf_rd_r=00JK8KDA3S1T2JRNBCVC&pf_rd_t=201&pf_rd_p=253457301&pf_rd_i=0821839675

20130517-015726.jpg

View original post

Universum Survey (Please help to do!)

Please try out this short survey. Your opinions are greatly appreciated.
Thanks for your help!

mathtuition88's avatarMathtuition88

Thanks for being a loyal reader of Mathtuition88.com!

Do you want to know which employer is the most suitable for you?

Please help to do this survey at:

Alternate URL: https://surveys.universumglobal.com/markets/singapore/distributions/ambWWCY

It is a Career Test by Universum. Participate to reveal your career type and discover the optimal employers for you!

Thanks for your help once again!

View original post

French & German’s Secondary School Maths Comparison

tomcircle's avatarMath Online Tom Circle

A French math teacher’s insight in math classes in Germany (15 years old = Secondary 3) and France (16/17 years old in Sec 4 & Pre-U / JC 1):

The French Math is more theoretical while the German Math (like English Math) is applied. So the result is Germany produces excellent precision engineers with Applied Math, while France produces 1/3 of the World’s Fields Medalists in theoretical Pure Math.

Many English GCE A-level top Math students from Singapore studying in French Universitues face the same dilemma: while their French Math professors think they are “weak” in Math (i.e. French abstract Pure Math), yet they beat the French classmates in Applied Math.

View original post

Einstein for Kids (Book)

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

Einstein, Relativity and Light for Kids

(Lulu Paperback link)

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.

An Ebook version is also available here:

Einstein, Relativity and Light for Kids

Excerpt:

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! 🙂

A Journey of Mathematics 数学之旅

tomcircle's avatarMath Online Tom Circle

Excellent free course for non mathematicians.

This Philosophical Math course has started half way but past videos are still hosted on the site.

The course is taught by prof Wang of Shanghai Jiaotong Technology University上海交通大学 (SJT), the Alma Mata of former China President Jiang (江泽民), Prime minister Chu (朱镕基), and Prof Qian XueSheng (钱学森) “The Father of Chinese Space and Missile” (China exchanged his country home return with USA FBI for 4 American generals from Korean War prisoners of War) who sent Chinese Taikongnauts (太空人) to space. 

SJT was formed initially as the ‘Classe Préparatoire’ (Bachelor degree, post-High school Prep-college) for graduate engineering to MIT,  while Qing Hua 清华 University was a prep-college for graduate Science/ Math to Harvard, Chicago, Cornell,  etc.

Go to Lesson 3: He explains from a game of Go what is “Space” in maths: Geometrical n-dimensional Space, Linear space, vector space.. why study functional space (in  which…

View original post 281 more words

A Mind For Numbers: How to Excel at Math and Science (Even If You Flunked Algebra)

Featured book:

A Mind For Numbers: How to Excel at Math and Science (Even If You Flunked Algebra)

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!

Mathematician’s Job: High Pay but Lowest Stress

One good reason to study Mathematics – high pay Mathematician job and lowest stress, comparing with other high-pay-high-stress professionals.

tomcircle's avatarMath Online Tom Circle

image

High pay high stress ?

Not really true … among the top 17 high-paying jobs (yearly earning above US $100,000) in the USA, Mathematician’s job has the lowest stress below 60 (in the scale from 0 no stress to highest stress at 100).

image
image

Source:
http://www.businessinsider.sg/high-paying-low-stress-jobs-2014-7/9/#.VAYQrYEZ7qA

View original post

Five things successful teachers do on the first day of class

math joke


Featured book:

Comic-Strip Math: Problem Solving: 80 Reproducible Cartoons With Dozens and Dozens of Story Problems That Motivate Students and Build Essential Math Skills

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.

 

ICM2014 Fields Medalist Manjul Bhargava

Correction (Thanks to Prof. Leong, see comments below):

“Manjul Bhargava’s PhD advisor is Andrew Wiles of Princeton University, not Benedict Gross. However, Bhargava is an undergraduate student of Gross in Harvard University.”

tomcircle's avatarMath Online Tom Circle

ICM2014 VideoSeries PL9: Manjul Bhargava:

(Part 1 of video – difficult part ): His PhD supervisor Benedict Gross (Harvard Math Dean) gave the laudation speech.

(Part 2 of video: Excellent and Understandable presentation) by the Fields medal 2014  receipient: the Canadian/American Indian Prof Manjul Bargarva.

View original post

Education News: School Starts Too Early?

Source: http://www.scientificamerican.com/article/school-starts-too-early/?&WT.mc_id=SA_WR_20140827

School Starts Too Early

The later high school classes start in the morning, the more academic performance improves
 

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

You are welcome to leave your comments below!


Featured book:

How Children Succeed: Grit, Curiosity, and the Hidden Power of Character

New Pedagogy: Math Without Word

tomcircle's avatarMath Online Tom Circle

When teaching Quadratic equation in Algebra class using the conventional math pedagogy, this is what you get …

image

Teaching Math without word, especially for autistic and dyslexic kids, using pictures, video games… look how easy is to explain difficult concepts – even for adults – why (-2)x (-3) = + 6 ?

image

http://www.transum.org/software/SW/YouTube/Video.asp?Movie=7odhYT8yzUM

View original post

Euler on Math Education

Today all school maths subjects are taught separately as: Arithmetic, Geometry, Trigonometry and Algebra, influenced by Euler in 1727.
Since 18th century Maths has evolved rapidly with the biggest revolution of Modern (Abstract) Maths in 19th century from the French prodigy Galois in Group Theory.

The 20th and 21st centuries Maths continues to expand from Galois Abstract Maths to a chaotic state where no single mathematician can claim to know all aspects of Maths like Newton, Euler, Gauss…did.
It is time to re-look at Euler’s outdated Maths pedagogy of 4 distinct disciplines… Can these 4 subjects be taught as ONE combined ‘Math’ (americans spell as singular) subject ?

tomcircle's avatarMath Online Tom Circle

Euler was invited by Peter I of Russia in 1727 to work in the
Petersburg Academy of Sciences. He introduced the fundamental math
disciplines in school math education:
1. Arithmetic
2. Geometry
3. Trigonometry
4. Algebra
these 4 are taught as separate and specific subjects, versus 19 duplicated disciplines in Europe.

Euler influenced not only in Russia schools, but in schools worldwide today.

Source: Russian Mathematics Education
Vol 1: History and world significance
Vol 2: Programs and practices
(Publisher: World Scientific)

View original post

Rational Trigonometry

tomcircle's avatarMath Online Tom Circle

UHG39: Rational trigonometry: an overview:

(Rational number only)

This is a revolutionary approach (2005) to teach Secondary / High school Trigonometry by using purely algebra, no geometry and no picture, no sine, cosine, tangent, etc.

New concepts:
Vector as an order pair (x, y)
Quadrance = magnitude of vector
Perpendicular of 2 vectors
Parallel
Spread (angle between 2 vectors)

Amazon Book by the Dr. NJ Wildburger:

image

View original post

The Best Universities in 35 Countries

tomcircle's avatarMath Online Tom Circle

http://www.businessinsider.sg/the-best-universities-in-every-country-2014-7/#.U9pB58kZ7qA

image

Australia: University of Sydney
Canada: University of Toronto
China: 北京大学
Japan: Tokyo University
Hong Kong: 香港大学
France:  Ecole Normale Supérieure,  Paris
India: Indian Institute of Technology, Delhi
Taiwan: 国立台湾大学
UK: Cambridge University
USA: Harvard University

View original post

Sum and Difference of Two Cubes

Students taking A Maths (Additional Maths) in 2014 should watch this: It may come out in the exam!

This is the newest addition to the new syllabus.


Featured book:

Practical Algebra: A Self-Teaching Guide, Second Edition

 

 

The Mandelbrot Set

Check out this video on the very interesting Mandelbrot Set:

Famously beautiful, the Mandelbrot Set is all about complex numbers. Featuring Dr Holly Krieger from MIT.


Featured book:

The Fractal Geometry of Nature

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.