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Proof based Calculus and Differential Equations #57

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1835253
Added Calculus with Theory)
ernest-mm Jun 12, 2025
99485f4
Added Multivariable Calculus with Theory
ernest-mm Jun 12, 2025
940d647
Replaced Differential Equations
ernest-mm Jun 12, 2025
daf5230
Added the MIT's Calculus 1 A, B and C courses to the math prerequisites
ernest-mm Jun 12, 2025
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7 changes: 5 additions & 2 deletions FAQ.md
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Expand Up @@ -20,7 +20,7 @@ Alternatively, you could [contribute](#CONTRIBUTING.md) an answer yourself.

### How can I review the math prerequisites?
Many OSSU students choose to review math topics that they have not studied recently.
OSSU recommends students use Khan Academy for such a review.
OSSU recommends students use Khan Academy for such a review (and MIT Open Learning Library for the Calculus part).
Below are links to topic assessments.
After taking an assessment, you should have a clear idea what topics to study, and resources on Khan Academy to use.

Expand All @@ -30,8 +30,11 @@ After taking an assessment, you should have a clear idea what topics to study, a
- [High School Math 1](https://www.khanacademy.org/math/math1#math1-subject-challenge)
- [High School Math 2](https://www.khanacademy.org/math/math2#math2-subject-challenge)
- [High School Math 3](https://www.khanacademy.org/math/math3#math3-subject-challenge)
- [MIT's Calculus 1A: Differentiation](https://openlearninglibrary.mit.edu/courses/course-v1:MITx+18.01.1x+2T2019/about)
- [MIT's Calculus 1B: Integration](https://openlearninglibrary.mit.edu/courses/course-v1:MITx+18.01.2x+3T2019/about)
- [MIT's Calculus 1C: Coordinate Systems & Infinite Series](https://openlearninglibrary.mit.edu/courses/course-v1:MITx+18.01.3x+1T2020/about)

(Math 1, 2, 3 covers all of algebra, pre-calculus, high school geometry, trig, stats. It interleaves the order of these topics.)
(High School Math 1, 2, 3 covers all of algebra, pre-calculus, high school geometry, trig, stats. It interleaves the order of these topics.)

### In what order should I take the courses?

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14 changes: 7 additions & 7 deletions README.md
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Expand Up @@ -115,23 +115,23 @@ Calculus is the study of change (differential calculus) and accumulation of quan

Courses | Duration | Effort | Prerequisites
:-- | :--: | :--: | :--:
[Calculus 1A: Differentiation](https://openlearninglibrary.mit.edu/courses/course-v1:MITx+18.01.1x+2T2019/about) | 13 weeks | 6-10 hours/week | [high school math](FAQ.md#how-can-i-review-the-math-prerequisites)
[Calculus 1B: Integration](https://openlearninglibrary.mit.edu/courses/course-v1:MITx+18.01.2x+3T2019/about) | 13 weeks | 5-10 hours/week | Calculus 1A
[Calculus 1C: Coordinate Systems & Infinite Series](https://openlearninglibrary.mit.edu/courses/course-v1:MITx+18.01.3x+1T2020/about) | 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
[Calculus with Theory](https://ocw.mit.edu/courses/18-014-calculus-with-theory-fall-2010/) | 13 weeks | 10-15 hours/week | [Introduction to Mathematical Thinking](README.md#Introduction-to-Mathematical-Thinking) and [high school math](FAQ.md#how-can-i-review-the-math-prerequisites)
[Multivariable Calculus with Theory](https://ocw.mit.edu/courses/18-024-multivariable-calculus-with-theory-spring-2011/) | 13 weeks | 10-15 hours/week | Calculus with Theory

### Introduction to Differential Equations
Differential equations describe the science of change: the route by which natural and man-made systems move from one state to another. Epidemics, population growth, and weather patterns are all modeled using differential equations. It provides us a mathematical language to describe physical, chemical, and biological systems and their evolution.

**Topics covered:**
`First-order ODEs`
`Second-order ODEs`
`Higher-order ODEs`
`Laplace Transforms`
`Fourier Series`
`The Laplace Transform`
`Linear Systems of ODE’s`
`Nonlinear Systems of ODE’s`

Courses | Duration | Effort | Prerequisites
:-- | :--: | :--: | :--:
[Differential Equations](https://ocw.mit.edu/courses/18-03sc-differential-equations-fall-2011/) | 14 weeks | 12 hours/week | Calculus 1C
[Honors Differential Equations](https://ocw.mit.edu/courses/18-034-honors-differential-equations-spring-2004/) | 13 weeks | 10-15 hours/week | Calculus with Theory

### Discrete Mathematics
Discrete mathematics is the mathematics of objects and ideas. It includes topics such as combinatorics, graph theory, and logic. The topics discussed here also form the basis of the field of computer science. For mathematics majors, a discrete math course is usually also a first introduction to formal proofs.
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