Discrete Maths is a study of things which are discrete, which means things which can be counted. Discrete Maths forms the basis of a lot of concepts in algorithms and Computer science in general. I am starting this #100DaysOfX which Discrete Maths, to have a sufficient understanding of the concepts. I am using resources from NPTEL, MIT OCW, and ArsDigita University.
The plan is to follow the 3 lectures mentioned in the references and the Rosen book on Discrete math.
Day 16 | Thursday 21 March 2019¶
Days Progress¶
- Just a revision of implication, exclusive OR.
Thoughts¶
Day 15 | Wednesday 20 March 2019¶
Days Progress¶
- Completed the logical inference lecture from NPTEL's Discrete Maths
Thoughts¶
-
Learned about:-
- logical inference for propositional calculus
- Fallacy
- logical inference for Quantifiers
- Normal Forms
- CNF
- DNF
- logical inference for propositional calculus
Day 14 | Tuesday 19 March 2019¶
Days Progress¶
- Revision of Preposition calculus from Rosen Book.
Thoughts¶
-
Books are easier to understand once, the concept is understood.
Day 13 | Monday 18 March 2019¶
Days Progress¶
- Revision of lecture 4 from NPTEL's Discrete Maths
Thoughts¶
- Learned that Implication and Equivalence are not the same.
-
Understood about logical relationship involving quantifiers.
Day 12 | Wednesday 13 March 2019¶
Days Progress¶
- Revision of lecture 4 from NPTEL's Discrete Maths
Thoughts¶
- Now learned properly about Predicates and Quantifiers.
- Scope of Quantifiers.
-
Valid,Satisfiableandunsatisfiablepredicates.
Day 11 | Tuesday 12 March 2019¶
Days Progress¶
- Again listened to the 4th lecture of NPTEL's Discrete Maths
Thoughts¶
-
Learned about Logical Inference.
Day 10 | Monday 11 March 2019¶
Days Progress¶
- Listened to the 4th lecture of NPTEL's Discrete Maths
- Learned a little about logical inference.
Thoughts¶
-
Still confusion over Predicate and Quantifiers.
Day 09 | Thursday 28 February 2019¶
Days Progress¶
- Reading and listening to explanation on how to negate a quantifiers.
- Learning about scope of a quantifiers.
Thoughts¶
-
Still have doubts on these topics.
Day 08 | Wednesday 27 February 2019¶
Days Progress¶
In between the 4th Lecture of NPTEL's Discrete Maths
Thoughts¶
- Great lecture on predicate logic
- Learned about:-
- Valid Expression
- Satisfiable Expression
- Unsatisfiable Expression
These addition video's also helped.
Day 07 | Tuesday 26 February 2019¶
Days Progress¶
Listened to the 2nd lecture of MIT 6.042J YouTube play-list
Thoughts¶
-
This lecture discusses about
- Proof by Contradiction
- Introduces to the concept of Induction proof.
Day 06 | Monday 25 February 2019¶
Days Progress¶
Completed the 3rd Lecture of NPTEL's Discrete Maths.
Thoughts¶
Today I learned about:-
-
Predicate and Quantifiers.
- Predicate
- Predicate Logic
- n-ary predicate
- Quantifiers
- Universal
- Existential
- Binding Variables
- Logical equivalence involving quantifiers.
- Predicate
Day 05 | Friday 22 February 2019¶
Today was a rest day for Discrete Maths.
Day 04 | Thursday 21 February 2019¶
Days Progress¶
- Listened to the 2nd lecture of MIT 6.042J YouTube play-list
- This lecture discusses about
- Proof by Contradiction
- Introduces to the concept of Induction proof.
Thoughts¶
-
Today was focused on listening to the lecture, so have not taken detailed notes.
Day 03 | Wednesday 20 February 2019¶
Days Progress¶
Completed the 2nd Lecture of NPTEL's Discrete Maths.
Thoughts¶
Today I learned about:-
- Proving implication without drawing all possible rows of truth table.
- Proved that implication is not associative.
- Learned about logical identities.
- Simplified complex compound propositions.
- Conversion between English to logic and vice versa.
-
Rules of inference
- Modus Ponens
- Modus Tollens
Day 02 | Tuesday 19 February 2019¶
Days Progress¶
- Complete the First lecture of MIT 6.042J YouTube play list
Thoughts¶
-
I have not taken any notes, but the lecture was mostly focused on methods of proof, propositions and connectives.
Day 01 | Monday 18 February 2019¶
Days Progress¶
- Complete the First lecture of NPTEL's YouTube play list .
Thoughts¶
This lecture covers these topics:-
- Logic
- Propositions
- Logical Connectives (\(\&\), \(|\), \(\sim\)) and its truth tables
- Implication. (\(\Rightarrow\))
- Equivalence. (\(\Leftrightarrow\))
- Tautology, Contradiction & Contingency.
- Logical Identities
Understanding Equivalence and Implication was little tough.
These 2 video's provided the additional help.
- Rachel's Discrete Math Course - Implications (Lecture 5)
- Propositional logic | first order predicate logic| Propositional calculus | gate | net - part 5
- Link to Tweet
Reference¶
- NPTEL | Computer Sc - Discrete Mathematical Structures | Prof. Kamala Krithivasan
- ArsDigita | Discrete Mathematics and Its Applications | Rosen | Shai Simonson
- MIT 6.042J | Mathematics for Computer Science, Fall 2010 | Tom Leighton, Marten van Dijk
- Amazon | Discrete Mathematics and Its Applications (SIE) | Kenneth Rosen
- Latex | Math Symbols
- Pelican and Math Equations