This will be my final post associated with the Analysis I course, for which the last lecture was yesterday. It’s possible that I’ll write further relevant posts in the nearish future, but it’s also possible that I won’t. This one is a short one to draw attention to other material that can be found on the web that may help you to learn the course material. It will be an incomplete list: further suggestions would be welcome in the comments below.

A good way to test your basic knowledge of (some of) the course would be to do a short multiple-choice quiz devised by Vicky Neale. If you don’t get the right answer first time for every question, then it will give you an idea of the areas of the course that need attention.

Terence Tao has also created a number of multiple-choice quizzes, some of which are relevant…

One of the hardest questions for many math teachers to answer in a way that is relevant to students is: “why do I need to know this?”  “For the next course you take”, the easiest answer in many cases, does not answer the question that was usually being asked.

My answers to this question obviously depend on the topic being studied at moment, and I don’t have “good” answers for all topics…  but here is my list of key quantitative life skills I learned directly or indirectly from math class, with

I didn’t encounter the Quadrilateral Midpoint Theorem (QMT) until I had been teaching a few years.  Following is a minor variation on my approach to the QMT this year plus a fun way I leveraged the result to introduce similarity.

In case you haven’t heard of it, the surprisingly lovely QMT says that if you connect, in order, the midpoints of the four sides of a quadrilateral–any quadrilateral–even if the quadrilateral is concave or if its sides cross–the resulting figure will always be a parallelogram.

This is a cool and easy property to explore on any dynamic geometry software package (GeoGebra, TI-Nspire, Cabri, …).

SKETCH OF THE TRADITIONAL PROOF:  The proof is often established through triangle similarity:  Whenever you connect the midpoints of two sides of a triangle, the resulting segment will be parallel to and half the length of the triangle’s third side…

Note:
China: 九章算术， 秦九韶
Persia : Algebra, Algorithm
Italy: Fibonacci

The millennium bug or the Y2K bug was going to cause planes to fall from the sky, bank accounts to be wiped out, electricity grids to cease functioning, trains to crash, cars to collide as stop lights stopped functioning, life support units to malfunction and computers to crash around the globe. For years leading up to midnight on New Years eve 1999 consults were paid extraordinary amounts of money to solve the problem.  When the clock ticked over to 1 ^st Jan 2000 nothing much happened. It was, indeed, a non-event, an error in logic.  (Pic from, appropriately, digyourowngrave.com)  

The Maths Error: Guessing the Answer.

Computer programmers represented the year in the date of many programs using two digits but claimed logical errors would arise upon “rollover” from x99 to x00.

While consultants claimed their advice saved the world from catastrophe countries that spent very little on the…

http://en.m.wikipedia.org/wiki/Ng%C3%B4_B%E1%BA%A3o_Ch%C3%A2u

Interview (in Chinese):

http://wk.baidu.com/view/2919f063caaedd3383c4d3a4?pcf=2#page/1/1388828375964

Dr. Yeo Ning Hong was the former cabinet Minister of Singapore. He wrote a few Math books after retirement to teach his grand-daughters in primary schools – on Trigonometric Identity Proofs !!!
Yes!
He has wonderful tricks to make such difficult Secondary 3 Math easy for kids, and of course, also helps the weak Math teenagers.

Interesting !
Trig Or Treat: An Encyclopedia of Trigonometric Identity Proofs With Intellectually Challenging Games

The other books by him are:

The Pleasures of Pi,e and Other Interesting Numbers

Memorize Trick For Ring:

1. Ring (R) is for Marriage with 2 operations: + (addition of kids), * (multiply asset).

2. (R , +) is Commutative Group
Analogy: your kids are also your wife’s kids, vice versa.

3. (R ,*) is Semi-Group (only closure & associative)
Analogy: your asset to multiply (*) is semi (50%) owned by your wife.

4. Fair distributive law for * with respect to +
=> distribute your asset (a) to your kids (k) & wife (w):
a*(k+w) = a*k + a*w

5. No division (/) operation => Ring can’t be broken.

A few weeks ago I wrote a post in shock at the fact that a number of schools in the locality had been teaching rounding wrongly. By this I don’t mean I took issue with their pedagogical approach, but rather that the method of rounding they were teaching was wrong and would result in the wrong answer in some instances. This post received the following comment from Old Andrew (@andrewolduk):

“Is anybody going to raise the obvious issue here that a lot of maths teachers don’t have maths degrees? In recent years the rise of “conversion courses” means that many have a background that isn’t in the least mathematical.”

This stirred up some quite strong feelings on both sides. Sophie Skinner (@miss_skinner) wrote this excellent piece stating her views, and Dave Gale (@reflectivemaths) wrote this piece reflecting his view. Twitter has been buzzing with conversation on the matter, and…

Description: *FREE app at time of post *  Sushi Monster is a ridiculously cute and engaging way to practice math fact fluency (addition and multiplication)!  Students must use their critical thinking and reasoning skills to strategically decide which sushi pieces (each has a number above it) to add/multiply together to feed the monster the total he desires.  Within each round, students see all the upcoming totals in the top left-hand corner so they can plan ahead.  Next to this bar is a Number Sentence bar that builds the addition/multiplication sentence as the student chooses sushi.  If it’s wrong, the monster throws a fit and tosses the sushi plates back!  (What a picky monster…)  Levels within this app are sequenced so that they become progressively more difficult as the student completes them.

Compatible with the following device(s): iPad, iPod Touch, and iPhone

Implementation in classroom:

– Activity idea:  This is a…

http://en.m.wikipedia.org/wiki/Paul_Erd%C5%91s

What is Erdős Number ?

Amazon Book: “My Brain Is Open”

Paul Erdős (er-dish) was one of the greatest mathematicians in 21st Century, a Jewish Hungarian, single and no home. He traveled around the world in one small suitcase containing his mathematical papers. He would knock at the door of his former students or math collaborator impromptu, started working and published the papers, then moved on to next destination the moment his overstay became unwelcome by the host’s wife. In this way he published 1,500 articles in his lifetime.

Example:

Einstein had the Erdős Number 2 , through his assistant who co-wrote a paper with Paul Erdős.

Ref:

http://tomcircle.wordpress.com/2013/03/30/paul-erdos/

Prof Benedict Gross is one of the best Algebra professors I have seen – he can explain so well the abstract concepts, without injecting fear and confusion to the students.

As Prof Gross had brilliantly said in the beginning of this Lecture 1:

Algebra is the language of Math.

Since Math is the language of science,
therefore any serious Science needs to speak in Algebra language.

Today, if you read a research paper on any math (or Computer Science, Mathematical Physics…) topic, hardly you can avoid these “basic” algebraic lingoes: Group, Ring, Field, Vector Spaces, Quotient Group, Ideal, …

I strongly recommend to anyone who likes to study Modern Algebra but afraid of the abstractness, this is the course (free) for you. I can guarantee you by the halfway (15th lecture) you will have a solid foundation, and by the last lecture you will be able to follow high-level…

$latex boxed{n!=int_{0}^{infty}x^{n}e^{-x}dx}$

For original post: < Click Here >

The romantic gallic Frenchmen like to joke and give pranks. We have already seen the Number 1 Mathematical ‘prank’ in Our Daily Story #1 (The Fermat’s Last Theorem), here is another 20th century Math prank “Nicolas Bourbaki” – the anonymous French mathematician who did not exist, but like Fermat, changed the scene of Modern Math after WW II.

http://en.m.wikipedia.org/wiki/Nicolas_Bourbaki

André Weil (not to confuse with Andrew Wiles of FLT in Story #2 ) and his university classmates from the Ecole Normale Supérieure (Évariste Galois‘s alma mater which expelled him for involvement in the French Revolution), wanting to do something on the outdated French university Math textbooks, formed an underground ‘clan’ in a Parisian Café near Jardin du Luxembourg. They met often to brainstorm and debate on the most advanced Math topics du jour. Finally they decided to totally re-write the foundation of Math based on Set…

Description: *FREE app*  Although Math vs Zombies is probably meant for children, I found this app to be really fun, especially if there were watching me play and screaming in anxiety!  Basically, cute/quirky zombies are coming to get you, and the only way to change them back into humans (and save yourself) is to solve math equations correctly.  There’s nothing like a little urgency to get those brain juices flowing! Students using this app can choose from four basic operations: addition, subtraction, multiplication, and division.  Within each Operation Level, there are six mini levels and a boss level to beat, and the equations become progressively more difficult between mini levels.  Also, the difficulty level can be set to easy, medium, or hard by clicking on the gear in the bottom left-hand corner of the main menu.

Compatible with the following device(s): iPad, iPod Touch, and iPhone

Implementation in classroom:

–…

The 3 valuable  takeaways from this 1- hour interview with Steve Ballmer, who co-founded Microsoft with the richest man in the world Bill Gates:

1. Have a great idea before startup.
– The financial,  talent, etc come later.

2. Great company does (at least) one trick well.
– Microsoft has 2.5 tricks: PC operating system (Windows); Microprocessors in data center (Winservers); the half trick is X box game console. 

– Apple also has 2 tricks: Mac; Mobile computing in iPhone/iPAD/Appstore

– Facebook (Social Network) and Google (Search Engine)  have 1 trick.

– Sony has 1 trick : Audio TV

– HP has 1 trick: Tester Equipment (now in Agilent)

– IBM has 1 trick: Entreprise Data Centre

– Samsung has 1 trick: hardware manufacturer (LCD flat panel, Smartphone…)

– Amazon has 1 trick: online bookshop

– Alibaba.com has 1 trick: eCommerce

Many great companies degenerate into smallness or extinction, because…

Remember that you can solve the puzzles from the League online on the Sudokucup Guest League page with a 24h delay (though I’m not certain whether this is too late to be put up today).

I’m sorry dearest readers, I think I’ll have to skip an explanation of why I’m inactive on my blog right now for later. There’s just too many plans right now, that all seem to end around May, and if it all goes as planned, you’ll see at least some of the reasons why I’ve been too busy to post here.

Anyway, here’s a Killer Sudoku that was used for the Polish Sudoku Championship qualifiers. These qualifiers were open to International solvers online, so I think many solvers would have seen this already. I still think it’s nice enough to put it up for those of you who haven’t.

Rules – Follow Classic Sudoku rules.
Additionally…