Category Archives: Algebra

Direct Sum vs Cartesian Product

Excellent explanation found on Math Stackexchange. Basically for finite index sets (finite number of factors), the two constructions are the same. Only when there is an infinite number of factors, the direct sum is the subgroup of the Cartesian product … Continue reading

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Useful Theorem in Introductory Ring Theory

Something interesting I realised in my studies in Math is that certain theorems are more “useful” than others. Certain theorems’ sole purpose seem to be an intermediate step to prove another theorem and are never used again. Other theorems seem … Continue reading

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A solvable group that has a composition series is necessarily finite

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Sylow subgroup intersection of a certain index + F1 Trespasser

Today, I read the news online, the latest news is that a man was strolling along the F1 track while the race was ongoing. Really unbelievable. Also, recently our recommended books from Amazon for GAT/DSA preparation have been very popular … Continue reading

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Singapore Haze & Subgroup of Smallest Prime Index

Recently, the Singapore Haze is getting quite bad, crossing the 200 PSI Mark on several occasions. Do consider purchasing a Air Purifier, or some N95 Masks, as the haze problem is probably staying for at least a month. Personally, I … Continue reading

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Quadratic Equations Questions and Answers

Quadratic Equations Questions and Solutions Today we will discuss about the quadratic equation . The way to derive the Quadratic Formula is to use completing the square. First, we divide throughout by a, where a is assumed to be non-zero … Continue reading

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Sum of roots and Product of roots of Quadratic Equation

Given a quadratic equation with roots and , we have: How do we prove this? It is actually due to the quadratic formula! Recall that the quadratic formula gives the roots of the quadratic equation as: Now, we can let Hence, … Continue reading

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Differentiation Rules

Today, we will recap the four basic rules of Differentiation: Differentiating Powers of x (Power comes down, and the remaining power reduced by 1) Chain Rule (i.e. times differentiate inside the bracket) Product Rule (Keep the first term X differentiate … Continue reading

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NUS Past Year Paper

This is a list of websites related to NUS Past Year Paper: 1) Official NUS Past Year Exam Paper website: http://libguides.nus.edu.sg/content.php?pid=227106&sid=1896904 2) NUS Physics Society Past Year Paper: http://physics.nus.edu.sg/~physoc/pyp.html 3) NUS Maths Society Past Year Paper: http://www.nusmathsociety.org/pyp.html

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The Lesson of Grace in Teaching

Source: http://mathyawp.blogspot.sg/2013/01/the-lesson-of-grace-in-teaching.html Excerpt: The Lesson of Grace in Teaching            From weakness to wholeness, the struggle and the hope Francis Edward Su MAA Haimo Teaching Award Lecture Joint Math Meetings, January 11, 2013 An audio file … Continue reading

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Google Page Rank 4

We are now at Google Page Rank 4 for our website!

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Secondary Four O Level Maths Tuition (E Maths & A Maths Tuition) at Bishan starting in 2014!

Maths Group Tuition starting in 2014! https://mathtuition88.com/group-tuition/ Secondary Four O Level Maths Tuition (E Maths & A Maths Tuition) at Bishan starting in 2014! Location: Block 230 Bishan Street 23 #B1-35 S(570230) Schedule: Monday 7pm-9pm Thursday 7pm-9pm (Perfect for students … Continue reading

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Make (y) the subject of the formulae (O Level Maths Tuition)

Question: Make (y) the subject of the formulae (1) Solution: Cross multiply,

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积少成多: How can doing at least one Maths question per day help you improve! (Maths Tuition Revision Strategy)

We all know the saying “an apple a day keeps the doctor away“. Many essential activities, like eating, exercising, sleeping, needs to be done on a daily basis. Mathematics is no different! Here is a surprising fact of how much … Continue reading

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How to avoid Careless Mistakes for Maths?

Many parents have feedback to me that their child often makes careless mistakes in Maths, at all levels, from Primary, Secondary, to JC Level. I truly empathize with them, as it often leads to marks being lost unnecessarily. Not to mention, it … Continue reading

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