Discussion on Oct, 7 2017.
Notes and references on Numbers and their constructions :
Notes: The detailed notes pertaining to the discussion will be uploaded soon.
References:
1. Naive Set Theory : Paul Halmos : This is a wonderful book to pick up once one is motivated as to Why study Mathematics and Axiomatic Set theory?, Why begin the study of Mathematics from Axiomatic Set Theory? (For both of which the contents of earlier discussion serves a good purpose) . A recommended reading, if one wants to skip chapters concerned with Cardinal Numbers, Ordinal Numbers and their arithmetic, would be chapters 1 - 16, 22 - 23.
Some Notes and Solutions.
Note:
After chapter 16, a good step is to complete the chain of Constructions of Numbers, which were briefly discussed during the discussion, for which the references are:
1. William Thurston : The Number System. (Main text).
2. Edmund Landau : Foundations of Analysis. (Occasional Reference).
3. Some great notes on Construction of Numbers that I found on the web:
This is an ideal route that serves as a prerequisite for studying Mathematical logic, Discrete Math, Mathematics for Computer Science etc. A good follow up for those who are interested in Mathematical Logic would be the NPTEL Course on Mathematical Logic by Prof. Arindama Singh.
Cheers!
-Karthik.
Notes on Special Relativity:
Please find below the notes on Special Relativity. Detailed description of talks dated Oct 7, 2017 will be uploaded soon.
https://drive.google.com/open?id=0B2Ag_BfedIaAWGJ1VFR1UDFLZmc
Note- In the last page of the notes, I have derived the exact transformation rule for a contravariant vector and a covariant vector, one can extend this to any mixed rank tensor. Sorry I forgot to write this line in the notes itself.
Cheers,
Arpit..
Notes: The detailed notes pertaining to the discussion will be uploaded soon.
References:
1. Naive Set Theory : Paul Halmos : This is a wonderful book to pick up once one is motivated as to Why study Mathematics and Axiomatic Set theory?, Why begin the study of Mathematics from Axiomatic Set Theory? (For both of which the contents of earlier discussion serves a good purpose) . A recommended reading, if one wants to skip chapters concerned with Cardinal Numbers, Ordinal Numbers and their arithmetic, would be chapters 1 - 16, 22 - 23.
Some Notes and Solutions.
Note:
After chapter 16, a good step is to complete the chain of Constructions of Numbers, which were briefly discussed during the discussion, for which the references are:
1. William Thurston : The Number System. (Main text).
2. Edmund Landau : Foundations of Analysis. (Occasional Reference).
3. Some great notes on Construction of Numbers that I found on the web:
This is an ideal route that serves as a prerequisite for studying Mathematical logic, Discrete Math, Mathematics for Computer Science etc. A good follow up for those who are interested in Mathematical Logic would be the NPTEL Course on Mathematical Logic by Prof. Arindama Singh.
Cheers!
-Karthik.
Notes on Special Relativity:
Please find below the notes on Special Relativity. Detailed description of talks dated Oct 7, 2017 will be uploaded soon.
https://drive.google.com/open?id=0B2Ag_BfedIaAWGJ1VFR1UDFLZmc
Note- In the last page of the notes, I have derived the exact transformation rule for a contravariant vector and a covariant vector, one can extend this to any mixed rank tensor. Sorry I forgot to write this line in the notes itself.
Cheers,
Arpit..
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