From 50de66f53ca4cc19d05d65b0c8bf816d92c6a0b3 Mon Sep 17 00:00:00 2001 From: Hassam Uddin Date: Sat, 19 Sep 2020 15:37:03 -0500 Subject: [PATCH 1/2] Create general layout, introductory mathematics I've tried to incorporate the various areas shown in the [mathematics roadmap](https://github.com/TalalAlrawajfeh/mathematics-roadmap), as well as everything required by the 2015 CUPM Curriculum. I'm not sure if "Introduction to Mathematical Thinking" would be considered enough to cover the history of mathematics requirements that the CUPM curriculum puts forth. These suggestions are just suggestions, and most likely, as we find courses and textbooks to cover them, the true structure of the repository will change. --- README.md | 59 +++++++++++++++++++++++++++++++++++++++++++++++++++++++ 1 file changed, 59 insertions(+) diff --git a/README.md b/README.md index e09d16a..948af8b 100644 --- a/README.md +++ b/README.md @@ -84,6 +84,65 @@ just remember that you can't purchase success! - [Statistics](https://www.edx.org/course/fundamentals-of-statistics) - Applications (**TODO**) +## Introductory Mathematics + +### Introduction to Mathematical Thinking +Most people's views of mathematics are destroyed in school by focusing on memorzation and regurgitation. Mathematics is anything but. This class covers how to think like a mathematician and solve problems. + +**Topics covered:** +`Mathematical mindset` +`Number Theory` + +Courses | Duration | Effort | Prerequisites +:-- | :--: | :--: | :--: +[Introduction to Mathematical Thinking](https://www.coursera.org/learn/mathematical-thinking) | 10 weeks | 4 hours/week | none + +### Calculus +Calculus is the foundation of our world, explaining the phenomena that underly our technology, our planets, and our hearts. + +**Topics Covered:** +`Derivatives` +`Integrals` +`Infinity` + +Courses | Duration | Effort | Prerequisites +:-- | :--: | :--: | :--: +[Calculus 1A: Differentiation](https://www.edx.org/course/calculus-1a-differentiation) | 13 weeks | 6-10 hours/week | high school math +[Calculus 1B: Integration](https://www.edx.org/course/calculus-1b-integration) | 13 weeks | 5-10 hours/week | Calculus 1A +[Calculus 1C: Coordinate Systems & Infinite Series](https://www.edx.org/course/calculus-1c-coordinate-systems-infinite-series) | 6 weeks | 5-10 hours/week | Calculus 1B +[Multivariable Calculus](https://ocw.mit.edu/courses/mathematics/18-02sc-multivariable-calculus-fall-2010/) | 12 weeks | 6 hours/week | Calculus 1C + +### Linear Algebra +Courses | Duration | Effort | Prerequisites +:-- | :--: | :--: | :--: +[Essence of Linear Algebra](https://www.youtube.com/playlist?list=PLZHQObOWTQDPD3MizzM2xVFitgF8hE_ab) | - | - | high school math +[Linear Algebra](https://ocw.mit.edu/courses/mathematics/18-06sc-linear-algebra-fall-2011/) | 14 weeks | 12 hours/week | Essence of Linear Algebra + +### Differential Equations +Courses | Duration | Effort | Prerequisites +:-- | :--: | :--: | :--: +Introduction to Differential Equations | 14 weeks | 3-6 hours/week | Calculus 1C +Differential Equations: 2x2 Systems | 8 weeks | 2-5 hours/week | Introduction to Differential Equations +Differential Equations: Linear Algebra and NxN Systems of Differential Equations | 12 weeks | 5-8 hours/week | Differential Equations 2x2 Systems, Linear Algebra +Differential Equations: Fourier Series and Partial Differential Equations | 11 weeks | 5-8 hours/week | Differential Equations: Linear Algebra and NxN Systems of Differential Equations +Transfer Functions and the Laplace Transform | 10 weeks | 3-6 hours/week | Introduction to Differential Equations + +## Mathematical Logic +These courses should include logic, set theory, number theory, and proofs + +## Geometry +Classical Geometry, Euclidian and non-Euclidian, introductory topology? + +## Probability and Statistics +Combinatorics, probability, statistics, game theory, applied stats + +## Mathematical Analysis +Real analysis, numerical analysis, complex analysis, optimization theory + +## Abstract Algebra +Abstract algebra, category theory, algebraic geometry and topology + + ## Congratulations After completing the requirements of the curriculum above, you will have completed the equivalent of a full bachelor's degree in Mathematics. Congratulations! From 4eef1118132c5e33fa8428fce79467c57ebe55b2 Mon Sep 17 00:00:00 2001 From: Hassam Uddin Date: Sun, 27 Sep 2020 18:45:55 -0500 Subject: [PATCH 2/2] Add links to Differential Equations courses --- README.md | 10 +++++----- 1 file changed, 5 insertions(+), 5 deletions(-) diff --git a/README.md b/README.md index 948af8b..fa10d6e 100644 --- a/README.md +++ b/README.md @@ -121,11 +121,11 @@ Courses | Duration | Effort | Prerequisites ### Differential Equations Courses | Duration | Effort | Prerequisites :-- | :--: | :--: | :--: -Introduction to Differential Equations | 14 weeks | 3-6 hours/week | Calculus 1C -Differential Equations: 2x2 Systems | 8 weeks | 2-5 hours/week | Introduction to Differential Equations -Differential Equations: Linear Algebra and NxN Systems of Differential Equations | 12 weeks | 5-8 hours/week | Differential Equations 2x2 Systems, Linear Algebra -Differential Equations: Fourier Series and Partial Differential Equations | 11 weeks | 5-8 hours/week | Differential Equations: Linear Algebra and NxN Systems of Differential Equations -Transfer Functions and the Laplace Transform | 10 weeks | 3-6 hours/week | Introduction to Differential Equations +[Introduction to Differential Equations](https://www.edx.org/course/introduction-to-differential-equations-2) | 14 weeks | 3-6 hours/week | Calculus 1C +[Differential Equations: 2x2 Systems](https://www.edx.org/course/differential-equations-2x2-systems) | 8 weeks | 2-5 hours/week | Introduction to Differential Equations +[Differential Equations: Linear Algebra and NxN Systems of Differential Equations](https://www.edx.org/course/differential-equations-linear-algebra-and-nxn-syst) | 12 weeks | 5-8 hours/week | Differential Equations 2x2 Systems, Linear Algebra +[Differential Equations: Fourier Series and Partial Differential Equations](https://www.edx.org/course/differential-equations-fourier-series-and-partial) | 11 weeks | 5-8 hours/week | Differential Equations: Linear Algebra and NxN Systems of Differential Equations +[Transfer Functions and the Laplace Transform](https://www.edx.org/course/transfer-functions-and-the-laplace-transform) | 10 weeks | 3-6 hours/week | Introduction to Differential Equations ## Mathematical Logic These courses should include logic, set theory, number theory, and proofs