Quantitative Reasoning II (Tools for Reasoning Skills)
This handout provides a comprehensive exploration of fundamental mathematical and logical concepts, making it an essential read for students and professionals alike. It begins with an introduction to enumeration and its practical applications, followed by an in-depth discussion on quantitative reasoning, number systems, and arithmetic operations. The book highlights the contributions of mathematicians, particularly Muslim scholars, in shaping the field. Logical reasoning and its significance in modern problem-solving are thoroughly examined, covering topics like propositions, truth tables, logical connectives, and set theory. Additionally, it delves into linear and non-linear models, equations, inequalities, and their real-world implications. The final section offers a detailed study of inferential statistics, data handling, and probability models, providing valuable insights into data analysis techniques.
We are really very thankful to Prof. Muhammad Usman Hamid for providing these notes and appreciates his effort to publish these notes on MathCity.org
- Name: Quantitative Reasoning II (Tools for Reasoning Skills)
- Author: Muhammad Usman Hamid
- Pages: 315 pages
- Format: PDF
- Size: 7.19 MB
Contents & Summary
- Introduction to Enumeration and its applications
- Introduction to quantitative reasoning
- Types of quantitative reasoning, Types of standard numbers system & basic arithmetic operations, The Base numbers system
- Overview of contributions of Mathematicians and Statisticians especially
- Muslim scholars
- Inductive reasoning, Deductive reasoning, Abductive Reasoning
- Logic and Its Applications
- Logical reasoning, importance and their application in modern age
- Propositions, prepositional variables
- Induction, deduction, logical connectives
- Compound statements, truth values, truth tables and applications,
- Negation, conjunction, disjunction
- Tautologies, contradiction and contingencies, equivalent statements
- The conditional and related statements
- Equivalent statements and logical equivalence
- Truth sets, a link between set theory and logic
- Arguments and their validity
- Categorical prepositions, Euler diagrams and Venn diagram
- Quantifiers and predicates, Logical fallacies and its types
- Linear and non-Linear Models
- Deterministic and population growth models
- Introduction to rectangular coordinates system
- Introduction to functions, their graphs and slopes
- Finding linear and non-linear models
- Exponential and Logarithmic functions
- Linear Equations and Inequalities
- Linear equation and its consequences
- Analytical approach to solve simultaneous equations
- Inequalities and their application
- Linear programming
- Inferential Statistics and Data Handlings
- Introduction to statistics, probabilistic models
- Data and distribution of data, tabulation
- Graph, stem and leaf diagram, charts, Misleading graphs, bivariate analysis
- Measuring relationships via regression analysis and correlation, Correlation and scatter plot
- Variability and measure of dispersion
- Data tendencies via measure of location and spread of data
- Box and whisker plot
- Sampling techniques, estimation, hypothesis and hypothesis testing