Reading List
The main objectives discussed here revolves around the complete acquisation/absorbtion of a list of materials in order to achieve a specific mindset, alas a Mathematical-Logical one. Therefore, we will learn how to achieve such fate by establishing a list of requirements and acquiring some as daily habits. We will also include a daily observation and updates on the development of such requirements.
List
At first, let us discuss the “acquisition levels” or rather, tiers. Such tiering system will allow us to check the development of our understanding of a current subject at hand.
Tiers
- Tier 0 : Vague notions about the current subject.
- Tier 1 : Very rudimental understanding, limited to an equivalent of reading a wikipedia article.
- Tier 2 : Slightly enhanced comprehension, full absorption of the basic principles - main axioms.
- Tier 3 : Enhanced notions, at this level we should have started to learn from textbooks.
- Tier 4 : First textbook reading completed, without exercices.
- Tier 5 : Complete textbook assimilation, including exercices.
- Tier 6 : Confirmation of the assimilated notions (exercies, practical applications).
- Tier 7 : Exploration of advanced concepts.
- Tier 8 : Complete understanding of the advanced concepts, including their potential applications.
- Tier 9 : Active learning about the subject, including communication with the experts in the field, and attending lectures/conferences.
Required Behavior :
In order to learn a huge amount of information, a required behavior must be followed :
- Cease all distractions.
- Establish a solid commitement to the task at hand.
- Introduce and use the mental palace effectively.
- Switch between multiple subjects within the day such as Microelectronics, Quantum Mechanics, Abstract Mathematics.
- Maintain perseverance and active learning.
- Stay on track and be patient about the material learned.
- Try to develop, and maintain momentum for a long period of time.
- Elaborate your focusing techniques.
- Implement ways of Logical/Mathematical Thinking in learning the required materials.
- Understand that total absorption of the materials learned are within incorporating your own mind within it (Total Immersion technique).
- Revoke unnecessary pervasive thoughts when acquiring the knowledge.
- Use the cumulative knowledge techniques : Any material learned for a day can ease the “route” for the rest.
- Develop long term concentration.
- Immerse the material learned, regardless of the time requirements at first hand. Develop the time management skills later on.
Short term reading list :
This list is meant to be completed ASAP :
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Axiomatic Set Theory.
Wikipedia article, an introduction paper about the subject, as well as my recommended book, a french book about the subject by Prof. Jean-Louis Krivine. -
Applied Analysis.
Wikipedia article, and the recommended book : Applied Analysis by John K. Hunter and Bruno Nachtergaele, from the Departement of Mathematics at University of California at Davis. The reading of such book derives from the absolute necessity to understand the following mathematical theories :
* Metric and Normed Spaces.
* Topological Spaces.
* Banach Spaces.
* Hilbert Spaces.
* When achieving the required tier, there’s a huge amounts of journals that can be read, one of which is the Abstract and Applied Analysis Journal. -
Mathematics of Quantum Mechanics.
Wikipedia article, I am also working on making some “course notes” out of the first chapter of Principles of Quantum Mechanics by Prof. Ramamurti Shankar, Yale University, New Haven.
Long term reading list :
This reading list will be completed on the long run, and once all of the short term list’s main subject have been well understood.
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Microelectronics (my field).
A subfield of electronics, it deals with integrated circuit design and analysis. One great book I recommend is the Design of Analog CMOS Integrated Circuits, by Prof. Behzad Razavi. -
Mathematical logic.
This could be straightfoward, and if the understanding of Axiomatic Set theory (ZFC) is complete, this task should be trival.Here’s the wikipedia article. One of the best compilations about Mathematical Logic as well as a complete study guide, an appendix of a collection of books, can be found at Peter Smith’s blog. -
Pure Mathematics.
Altho an engineer, it is certainly clear that a mathematical emphasis will represent a great aid in future careers. Here’s a complete compilation of mathematical books about concepts in Pure Mathematics. -
Quantum Physics.
The wikipedia’s well written article, as well as my recommended book, which contains all the machinary needed to understand the theory. There’s also Prof. Richard Feynman’s book about Quantum Electro-Dynamics. -
General Relativity.
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Neuromorphic Engineering.
List about Advanced Concepts :
A life-long reading list :
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Quantum Field Theory. Wikipedia article. an introduction paper (french), as well as the books I recommend(french) and the other one too.
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Theoretical Physics. Wiki Article, and a comprehensive compilation by Nobel prize winner Prof. Gerard’t Hooft.
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Nanoelectronics.
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Computer Architecture and theoretical computer science.
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Neuroscience.