Critical Thinking
Mathematics, Logic
Shiv Nadar University via Swayam
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Overview
This is a course has length of 10 hours. The course is subdivided into 5 separate modules. A student opting for this course should follow the following path:
1. Set Theory (2 hours)
This module introduces the basic of naïve set theory. This allows us to develop a language that can be used to understand various concepts of Logic. This module is of two hours. Students should go through the lecture notes and try to answer the questions provided in the question bank. When students are satisfied with their understanding of the material, then can take the quiz to test their understanding.
2. Theory of Numbers (1 hour)
This module introduces students to the basic of the theory of numbers. Students learn about the natural numbers, integers, rational numbers and real numbers. These concepts will help us to crate examples that explain various concepts of logic. The students are also introduced to mathematical induction: a technique used to prove various results about natural numbers.This module is of one hour. Students should go through the lecture notes and try to answer the questions provided in the question bank. When students are satisfied with their understanding of the material, then can take the quiz to test their understanding.
3. Constants and Variables (1 hour)
This modules explains the concept of a sentence. It explains how a concept of a sentence in logic is different from a sentence used in everyday language. It introduces the related concepts of a designatory function and a sentential function. It explains how variables in a sentential function can be replaced by constants to construct sentences. It also discusses the role of quantifiers in the construction of sentences.This module is of one hour. Students should go through the lecture notes and try to answer the questions provided in the question bank. When students are satisfied with their understanding of the material, then can take the quiz to test their understanding.
4. Sentential Calculus (4 hours)
This module starts by introducing students to the use of logical conjunctions like ‘not’, ‘or’, ‘and’ & ‘if…, then…’. It explains the concepts of argument, premise and conclusion. Students are taught to use truth tables to establish laws of sentential calculus.This module is of four hour. Students should go through the lecture notes and try to answer the questions provided in the question bank. When students are satisfied with their understanding of the material, then can take the quiz to test their understanding.
5. Theory of Relations (2 hours)
This module introduces the concept of binary relations. The concepts of domain and co-domain are explained. The module then explains the algebra of relations: operations through which new relations can be constructed from existing relations. In this context, we discuss some special relations like the universal relation and the null relations. The module also discusses the concepts of reflexive relations, transitive relations, symmetric relations etc.
Taught by
Partha Chatterjee