Coursework
1. Mathematical Thinking in Computer Science
Course Link: Mathematical Thinking in Computer Science
Topics:
Recursion
Induction
Logic
Invariants
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.
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2. Algebra: Elementary to Advanced
Course Link: Algebra Specialization
Topics:
Solving equations and inequalities
System of equations
Functions and their properties
Inverse functions
Exponentials and Logarithms
Polynomials and their roots
Summary:
This three-course specialization offers a structured introduction to core algebraic concepts. The first course focuses on foundational topics such as equations and inequalities. The second course explores functions in depth, covering their properties, transformations, and inverses. The third course introduces exponential and logarithmic functions, techniques for graphing them, and explores polynomials along with methods for finding their roots.
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3. Precalculus through Data and Modelling
Course Link: Precalculus
Topics:
Functions and their graphs
Periodic Functions
Linear Modelling
Exponential Modelling
Dimensional Analysis
Summary:
This specialization introduces fundamental Precalculus concepts across three courses. The first course, Relations and Functions, covers basic functions, equations of lines and quadratics, and exponential and logarithmic functions. The second course, Periodic Functions, explores trigonometric functions, their graphs, and key identities. The third course, Mathematical Modelling, focuses on applying concepts through linear and exponential modelling and dimensional analysis.
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4. 18.01x - Single Variable Calculus
This series provides an introduction to the mathematical notation, physical meaning, and geometric interpretation of various calculus concepts. Alongside developing fundamental computational skills, the series also provides an insight into real-world applications of these mathematical ideas.
Course 1 - Differentiation
Summary:
This course provides a comprehensive introduction to the concept of the derivative. It covers its mathematical notation, physical meaning, and geometric interpretation, enabling to move fluently between these different representations. Participants learn how to differentiate a wide range of functions and develop strong intuition for sketching their graphs. The course also introduces linear and quadratic approximations to simplify complex computations and build a deeper understanding of system behavior. Additionally, it explores techniques for maximizing and minimizing functions to optimize key properties such as cost, efficiency, energy, and power.
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Course 2 - Integration
Summary:
This course explores integral calculus through practical and thought-provoking questions, such as determining the optimal length of a spoon handle to prevent burns, or examining shapes with finite volume but infinite surface area. Learners investigate real-world applications, like how rider weight affects zip line trajectories, while gaining a solid understanding of the integral as the area under a graph and its relationship to derivatives. The course covers both functions that require computational integration and techniques for manual integration. Emphasizing the integral's importance across engineering, science, probability, and statistics, it highlights applications such as calculating centers of mass, analyzing beam stress, estimating motor power, and determining the distance traveled by rockets.
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