Mathematics

 

Academic Year 2017/8:

I am a Warwick Mathematics Society (WMS) Mentor in this academic year. The following lists the details of what we covered in our past sessions: (in descending chronological order)

 

  • 10.03.2018 Afternoon&Eve:
    • This is the warm up sheet.
    • We started with Question 1-4 of the warm up sheet, then reviewed Sections 4-5 of  MA106 Linear Algebra. Make sure you memorise the axioms prior to the exam.
    • We highlighted parts of Sections 6-7 of MA106 Linear Algebra,  then proved two important statements on Matrix Algebra. Notice that, “A only if B” means A implies B rather than the other way around.
    • A useful technique is, when you are confused or stuck at some given statements, try to plug in some numbers, e.g. n=2 and m=3, then try to see more generality through numerical operations. In particular, for complications like row-reduced forms, this technique may be helpful for at least a sketchy proof.
    • Here is the script I wrote, which covers most of the content.

 

  • 27.02.2018 Eve:
    • We reviewed some key concepts from Abstract Algebra, including the idea of field extensions from N to Z, Q, R, and further to R^k and R^{m*n}.
    • We went through the Sections 4-5 of  MA106 Linear Algebra.
    • We also went through a particular proof regarding the invertability of row operations, leading to a useful statement: A~B with B~C implies A~C.
    • Here is the script I wrote, which covers most of the content.

 

  • 06.12.2017 Afternoon&Eve:
    • We reviewed Euclidean Algorithm, fundamental set theory, and subgroups of Z.
    • We went through the Sections 2-4 of MA132 Foundations.
    • We went through some fundamental properties of sets as well as subgroups of Z, and used the results to understand modular arithmetic, Euclidean Algorithm and its extension, and finally went through some properties of eventual periodicity and rational numbers.
    • There were a few examples including the intuition behind binary set {0,1} and its computation that are not on the script.
    • Here is the script I wrote, which covers some of the content we went through.

 

  • 22.11.2017 Afternoon:
    • We reviewed Principle of Induction and other fundamental techniques in mathematical proofing.
    • We went through the Section 2 of MA132 Foundations.
    • We went through the proof of Fundamental Theorem of Arithmetic.
    • Unfortunately, all of the notes were written on the blackboard.
    • Here is the script I wrote, which is the plan for this session and the next one.