## Friday, June 24, 2016

### Profile

Hello,
I teach mathematics at the University of Hertfordshire. To contact me send an email to

k.singh@herts.ac.uk.
My Homepage is at http://mathsforall.co.uk/

Linear Algebra Step by Step:
http://www.oup.co.uk/companion/singh

In general I will be writing articles about mathematics, in particular adding comments to the book "Engineering Mathematics through Applications"

Kuldeep said...

I have just finishing marking resit exams and the most common mistake in all exams is not answering the question. Why does this serious error occur every year?

Kuldeep said...

Just been to a conference at Loughborough University and there seems to be so many different mathematical educational experts which are really developing the subject (mathematics) into unknown territory.
I personally think all that technology can provide is to motivate individuals. The ONLY way to learn mathematics is to DO mathematics.
This subject is not a spectator sport.

Kuldeep said...

Teaching what is meant by a surjective function is a real challenge. Most students can show a given function is injective but showing surjection seems a lot more difficult.

Kuldeep said...

Writing notes on supremum and infimum which students find very difficult to grasp. I wonder if it might be better just to use the terms Least Upper Bound and Greatest Lower Bound rather than the latin based supremum and infimum respectively.

Kuldeep said...

Just marked the Foundations of Mathematics workbook. Some concerns of the work is as follows:
Functions
The part on surjection of a function was not done well. Only need to select an element in the codomain and show that the function f does not map to it.
Proof by Induction
Most students prefer to expand rather than factorize their results which can be difficult in proving a given result by induction. I assume they do this automatically because it is the first thing that comes to their head. It is important to look at the final goal in prove by induction and then carry out the appropriate action on the result.
Proofs
Many mathematics students don’t like to write words but when writing a proof you need to be familiar with what is required. It is always good to finish a proof by the words “hence the result follows …”
Just because a result works for some numbers does not mean that it holds for all the numbers. To prove a result it is not good enough just to try some numbers and conclude the general result holds.
Common Mistakes
Composition of Functions - fof does not equal fxf
Simple algebraic mistakes such as not using the rules of indices when carrying out proof by induction.

Kuldeep said...

Used Smirk for the first time to teach my engineering class. Steve Bennett who was one of the developers (David Kraithman being the other) helped set everything up. It took a good half hour to set up. I will have to wait and see if this is a useful tool to use for teaching.

Kuldeep said...

I manage to fall off my bike today as I was going around a bend.

Kuldeep said...

Used Smirk again. It is one of the best softwares to use for the teaching of mathematics because you can construct your mathematics.

Anonymous said...

What is smirk?

Kuldeep said...

Smirk is a teaching tool which saves your work on the pc and records your voice. I use it to deliver my lectures by writing my notes on a tablet pc and speaking simultaneously. Students can then view this lecture on the web at the following url:
http://homepages.feis.herts.ac.
uk/~matqkks/lectures/

Kuldeep said...

Again just marked the number theory test and some of them have not answered the question.

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alittle background i was orignily not a smart kid so went round the other side and became a really bad kid who failed alot of subjects went collage cause thats all i could get in to, few years past i got a diploma in electronical engineering (did electronics cause like fixing stuff) and got in to city london university failed really bad maily due to very bad maths skills now im in coventry university and passed my first year with a 1st as maths was not an issue for me as i had the worlds best book

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