Discrete Structure
Lecturer: Dr. Suhaila binti Mohamed Yusuf
Since I always have a attraction to mathematics and this subject is related to maths, It makes me feel better to study computer science (software), so that what was the reason I wanted to study a bit about it.
This subject Discrete Structure is consisted of five courses; Mathematical Thinking in general(mostly puzzles), Combinatorics and Probability, Graph Theory, and Number Theory and Cryptography. At first, I heard that the courses had no prerequisite rather than basic math and curiosity about the topics alongside some of Python knowledge. How ever, for me, some math-y topics were interesting for me, so I watch videos , and do a bit of extra research about the details. The courses provide many puzzles and cording implements exercise as well as quizzes to have a dipper understanding of the topics. Especially the lecturer show examples with Python codes, which not only help better understanding but also let the students see the potential of the language itself while being more familiar to it. In the cording exercises, they provide some basic structures to start with, so it was not absolutely difficult for them by oneself. The lecturer also very kindly help inquires by the discussion forum, to help if there is any question or obstacle through the learning.
I am happy that I now have a little bit of experience about the many interesting topics so I could have a better mindset when I face problems in the future. I hope I now have less fear for my study, and I could have some more chance to study a bit more about Discrete Structure and related topics.
Foundations and logic for DS
Foundations and logic
Why: This is the assembly language of mathematics—the stuff at the bottom that everything else compiles to.
• Propositional logic.
• Predicate logic.
• Axioms, theories, and models.
• Proofs.
• Induction and recursion.
1.4.2 Basic mathematics on the real numbers
Why: You need to be able to understand, write, and prove equations and inequalities involving real numbers.
• Standard functions and their properties: addition, multiplication, exponentiation, logarithms.
• More specialized functions that come up in algorithm analysis: floor, ceiling, max, min.
• Techniques for proving inequalities, including:
– General inequality axioms (transitivity, anti-symmetry, etc.)
– Inequality axioms for R (i.e., how < interacts with addition, multiplication, etc.)
– Techniques involving derivatives (assumes calculus) (*):
∗ Finding local extrema of f by solving for f
0(x) = 0. (*)
∗ Using f00 to distinguish local minima from local maxima. (*)
∗ Using f 0 (x) ≤ g 0(x) in [a, b] and f(a) ≤ g(a) or f(b) ≤ g(b) to show f(x) ≤ g(x) in [a, b]. (*)
• Special subsets of the real number: rationals, integers, natural numbers