Coursework
Mathematical Thinking in Computer Science
Course Link: Mathematical Thinking in Computer Science
Summary
The course introduces the basic mathematical concepts that are applied in computation. The introduction focuses on breadth over depth. The course required basic programming knowledge as the topics were taught and tested using Python. The ideas were easily transferable to programming and helped to improve my programming skills.
Topics include
- Recursion
- Induction
- Logic
- Invariants
Documentation
Algebra: Elementary to Advanced
Course Link: Algebra: Elementary to Advanced Specialization
Summary
The specilization provides introduction to the elementary algebraic concepts of equations, inequalities. It also introduces the concept of functions and provides a tour of the classic set of functions and their properties like shifting, odd and even, graphing functions. Polynomials and their behavioural properties depending on their degree and finding roots along with graphing techniques.
Course 1 - Equations and Inequalities
- Structure of Number System
- Solving Equations
- Solving Inequalities
- System of Equations
Course 2 - Function and Applications
- Introduction to Functions
- Properties of Functions
- Inverse Functions
Course 3 - Polynomials and Roots
- Exponential and Logarithms
- Polynomials
- Roots of Polynomials
Documentation
Precalculus
Course Link: Precalculus through Data and Modelling Specialization
Summary
This specialization involves introductory concepts of Precalculus which has been divided into three courses.
Course 1 - Relation and Functions
- Basic and Common Functions
- Equations of Lines and Quadratics
- Exponential and Logarithmic Functions
- Properties of Logarithms
Course 2 - Periodic Functions
- Periodic Functions
- Right Triangle Trigonometry
- Sine and Cosine as Periodic Functions
- Tangent and Other Periodic Functions
- Identities of Periodic Functions
Course 3 - Mathematical Modelling
- Linear Modelling
- Exponential Modelling
- Dimensional Analysis
Documentation
Introduction to Calculus
Course Link: Introduction to Calculus
Summary
The focus and themes of the Introduction to Calculus course address the most important foundations for applications of mathematics in science, engineering and commerce. The course emphasises the key ideas and historical motivation for calculus, while at the same time striking a balance between theory and application, leading to a mastery of key threshold concepts in foundational mathematics.
Documentation
18.01x - Single Variable Calculus
Series Link: 18.01x
Overview
In this series, you will learn the mathematical notation, physical meaning, and geometric interpretation of a variety of calculus concepts. Along with the fundamental computational skills required to solve these problems, you will also gain insight into real-world applications of these mathematical ideas.
Course 1 - Differentiation
Summary
But what is the derivative? You will learn its mathematical notation, physical meaning, geometric interpretation, and be able to move fluently between these representations of the derivative. You will discover how to differentiate any function you can think up, and develop a powerful intuition to be able to sketch the graph of many functions. You will make linear and quadratic approximations of functions to simplify computations and gain intuition for system behavior. You will learn to maximize and minimize functions to optimize properties like cost, efficiency, energy, and power.
Documentation
Course 2 - Integration
Summary
Exploring integral mathematics to answer practical questions: How long should a spoon handle be to prevent burns while mixing fondue? Can we find a shape with finite volume but infinite surface area? Investigate how rider weight affects zip line trajectory. Understand the integral as an area under a graph and its connection to derivatives. Grasp functions demanding computer integration and techniques for manual integration. Crucial in engineering, science, probability, and statistics, integrals help find mass centers, beam stress, motor power, and rocket distance traveled.
Documentation
Lectures
Pre-Algebra
This lecture series introduces topics that prepare the learner for further lessons in Algebra. The topics include:
- Introduction to the Number Line
- Operations involving Integers
- Solving basic equations
- Introduction to Fractions
- Introduction to Rates and Ratios
- Operations with Polynomials
Supplementary Textbook: Prealgebra by Elayn Martin-Gay
Intermediate Algebra
This lecture series builds upon the concepts introduced in the previous series and develops methods like Factoring, Plotting, Inequalities and Exponentials.
- Factoring Basic Polynomials
- Rational expressions and Rational equations
- Plotting on Coordinate Plane
- Inequalities and Absolute Value Equations
- Radicals and Radical equations
- Working with Quadratic equations
- Exponential and Logarithmic equations
- Conic Sections
Supplementary Textbook: Intermediate Algebra by Elayn Martin-Gay
College Algebra
This supplementary lecture series provided by UMKC deals with topics in algebra that are need to be mastered before heading into Calculus.
- Functions
- Plotting Functions on Coordinate Plane
- Finding Zeros of Polynomials
- System of Equations
- Series and Sequence
Supplementary Textbook: College Algebra by Robert Blitzer
Books