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README.md: extracted some resources to basic maths section and moved advanced topics to the appendix

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@@ -207,38 +207,6 @@ Similar to other professions, embedded engineers require soft skills that can't
- [📝 Soft Skills For Embedded Systems Software Developers](https://www.embeddedrelated.com/showarticle/1470.php)
- [📝 10 Skills Every Embedded Engineer Should Have](https://medium.com/@lanceharvieruntime/10-skills-every-embedded-engineer-should-have-dcb867095b91)
_________________
### ✳️ Discrete Mathematics
A common subject that is essential to Computer Science students and some Math/Electrical Engineering Majors based on the [Assoication For Computing Machinery Guidelines for CS/CE education](https://www.acm.org/education/curricula-recommendations). It houses the most essential subjects for _abstract mathematical modelling_ and _theory of computation_. Furthermore, it helps students to establish the essential engineering mindset that represents the common basis among all computer science and computer engineering domains. However, Logic, Theory of combinatorics, Coding Theory, and Theory of Computation are among the most essential subjects for Embedded Systems Engineer.
_**Goal of learning Discrete Mathematics:**_ Embedded Systems Engineer should be able to grasp most of these information sooner or later based on their subspeciality (e.g., Coding Theory for Audio/Video Encoding/Decoding and Data Transmission - Automata Theory for event control and data transmission - Logic for digital circuit design and switching algebra - $$\Pi$$ Calculus and Automata Theory for Concurrency Modelling).
_Discrete Mathematics_ is a multi-semester course that involves subjects about the theoretical mathematical basis of computer science, including but not limited to:
* 🔵 Logic (Propositional, Quantificational and Normal Forms).
* 🔵 Axiomatic Set Theory (Sets, Operations on sets, and Power Sets).
* 🔵 Relation Sets and Function Theory (i.e., $$\lambda$$ Calculus).
* 🔵 Theory of combinatorics.
* 🔵 Matrix and Graph Theory.
* 🔵 Theory of computation (i.e., Computational Automata Theory, Computational Complexity, and Computational Computability).
* 🔵 Automata Theory (e.g., Finite-state Machines, Pushdown Automata, Turing Machines, and Cellular Automata).
* 🔵 Process Modelling/Calculi (i.e., $$\pi$$ Calculus).
* 🔵 Coding Theory.
* 🔵 Division Theorem Modular Arithmetics (Parts of Number Theory).
- [🎞️ Free Courses on Coursera](https://www.coursera.org/search?query=Discrete%20mathematics&topic=Computer%20Science&topic=Math%20and%20Logic&sortBy=BEST_MATCH)
- [📘👶 Open Access Books by LibreTexts](https://math.libretexts.org/Bookshelves/Combinatorics_and_Discrete_Mathematics)
- [📘👶 Essential discrete mathematics for computer science by Lewis HARRY., Zax R. ACM DL](https://dl.acm.org/doi/book/10.5555/3388468)
- [📘👶 Guide to Discrete Mathematics by Gerard O'Regan, Springer](https://link.springer.com/book/10.1007/978-3-030-81588-2)
- [📘💎 Discrete Mathematics and its applications by Rosen](https://dl.acm.org/doi/book/10.5555/579402)
- [📘💎 Discrete Mathematics with Applications by Susanna S. Epp](https://dl.acm.org/doi/book/10.5555/1941983)
- [📘💎 Switching and Finite Automata Theory, Cambrdige Press](https://dl.acm.org/doi/10.5555/1708070)
- [📘💎 Discrete Mathematical Structures by Bernard Kolman](https://www.pearson.com/en-us/subject-catalog/p/discrete-mathematical-structures-classic-version/P200000006227/9780137538782?srsltid=AfmBOooBdohmNtq7Wu42tHwSt7lUma46hBmKjqk8XJ8NNI6sf2-4-1kg)
- [📘💎 Bridge to Abstract Mathematics, AMS](https://bookstore.ams.org/view?ProductCode=TEXT/22)
- [📘💎 Invitation to Discrete Mathematics, Oxford University Press](https://global.oup.com/academic/product/invitation-to-discrete-mathematics-9780198570431?cc=eg&lang=en&)
- [📘💎 The Mathematics of Cellular Automata by Jane Hawkins, AMS](https://bookstore.ams.org/stml-108)
_________________
### ✳️ Electronics
@@ -246,8 +214,13 @@ _________________
#### 🔵 Basic Math & Calculus
- [🎞️ Khan Academy - Calculus 1](https://www.khanacademy.org/math/calculus-1)
- [🎞️ Free Courses for discrete mathematics on Coursera](https://www.coursera.org/search?query=Discrete%20mathematics&topic=Computer%20Science&topic=Math%20and%20Logic&sortBy=BEST_MATCH)
- [📘👶 Calculus For Dummies - Mark Ryan](https://a.co/d/cyvZqE1)
- [📘💎 Thomas' Calculus](https://a.co/d/gFcCC37)
- [📘👶 Open Access Discrete Mathematics Books by LibreTexts](https://math.libretexts.org/Bookshelves/Combinatorics_and_Discrete_Mathematics)
- [📘👶 Essential discrete Mathematics for computer science by Lewis HARRY., Zax R. ACM DL](https://dl.acm.org/doi/book/10.5555/3388468)
- [📘👶 Guide to Discrete Mathematics by Gerard O'Regan, Springer](https://link.springer.com/book/10.1007/978-3-030-81588-2)
- [📘💎 Bridge to Abstract Mathematics, AMS](https://bookstore.ams.org/view?ProductCode=TEXT/22)
#### 🔵 Principles of Electric Circuits
@@ -1467,6 +1440,32 @@ AUTOSAR, or AUTomotive Open System ARchitecture, is a global industry standard f
- [🎞️ Introduction to AUTOSAR](https://www.youtube.com/watch?v=NfZI8wvgZPo)
- [🎞️ Udemy - Autosar Architecture (Learn from Scratch with Demo)](https://www.udemy.com/course/autosar-architecture/)
_________________
### ✳️ Rigorous Mathematics: Discrete Mathematics
A common subject that is essential to Computer Science students and some Math/Electrical Engineering Majors based on the [Assoication For Computing Machinery Guidelines for CS/CE education](https://www.acm.org/education/curricula-recommendations). It houses the most essential subjects for _abstract mathematical modelling_ and _theory of computation_. Furthermore, it helps students to establish the essential engineering mindset that represents the common basis among all computer science and computer engineering domains. However, Logic, Theory of combinatorics, Coding Theory, and Theory of Computation are among the most essential subjects for Embedded Systems Engineer.
_**Goal of learning Discrete Mathematics:**_ Embedded Systems Engineer should be able to grasp most of these information sooner or later based on their subspeciality (e.g., Coding Theory for Audio/Video Encoding/Decoding and Data Transmission - Automata Theory for event control and data transmission - Logic for digital circuit design and switching algebra - $$\Pi$$ Calculus and Automata Theory for Concurrency Modelling).
_Discrete Mathematics_ is a multi-semester course that involves subjects about the theoretical mathematical basis of computer science, including but not limited to:
* 🔵 Logic (Propositional, Quantificational and Normal Forms).
* 🔵 Axiomatic Set Theory (Sets, Operations on sets, and Power Sets).
* 🔵 Relation Sets and Function Theory (i.e., $$\lambda$$ Calculus).
* 🔵 Theory of combinatorics.
* 🔵 Matrix and Graph Theory.
* 🔵 Theory of computation (i.e., Computational Automata Theory, Computational Complexity, and Computational Computability).
* 🔵 Automata Theory (e.g., Finite-state Machines, Pushdown Automata, Turing Machines, and Cellular Automata).
* 🔵 Process Modelling/Calculi (i.e., $$\pi$$ Calculus).
* 🔵 Coding Theory.
* 🔵 Division Theorem Modular Arithmetics (Parts of Number Theory).
- [📘💎 Discrete Mathematics and its applications by Rosen](https://dl.acm.org/doi/book/10.5555/579402)
- [📘💎 Discrete Mathematics with Applications by Susanna S. Epp](https://dl.acm.org/doi/book/10.5555/1941983)
- [📘💎 Switching and Finite Automata Theory, Cambrdige Press](https://dl.acm.org/doi/10.5555/1708070)
- [📘💎 Discrete Mathematical Structures by Bernard Kolman](https://www.pearson.com/en-us/subject-catalog/p/discrete-mathematical-structures-classic-version/P200000006227/9780137538782?srsltid=AfmBOooBdohmNtq7Wu42tHwSt7lUma46hBmKjqk8XJ8NNI6sf2-4-1kg)
- [📘💎 Invitation to Discrete Mathematics, Oxford University Press](https://global.oup.com/academic/product/invitation-to-discrete-mathematics-9780198570431?cc=eg&lang=en&)
- [📘💎 The Mathematics of Cellular Automata by Jane Hawkins, AMS](https://bookstore.ams.org/stml-108)
## History
At first this was meant to be my personal reading list but as the list gradually became bigger and bigger, I wondered why not share it with others. So I did research on current job postings for embedded engineering roles, selecting the most frequent skills and including them on a roadmap. In order to make the roadmap more comprehensive I also added some basic skills and finally came up with what you see here.