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A Summer of Maths (ASoM) 2016

A Summer of Maths 2016

Purpose of this thread

This thread should serve as an interactive resource to help people bridge the gap to undergraduate mathematics. I anticipate people will be discussing topics covered in a typical undergraduate course with emphasis on, though certainly not limited to, the first years of those respective courses. People should feel free to have tangential discussions including everything from the philosophy of mathematics to more practical things like choosing modules and subject areas. That said, we should aim to avoid discussing A-level material as well as topics from postgraduate courses as these will be of little interest to the majority of people participating in this thread. Also, most of the content here is taken from JKN's original post and all credit goes to him. :smile:

Target audience

I am assuming that the majority of people participating will be those who are currently preparing for the first year of their undergraduate course in mathematics at Cambridge. That said, this thread is in no way exclusive and so I hope that everybody feels welcome! This is also why I am choosing to use the topic headings for the Cambridge mathematics course as the basis for the resource library. I hope that many do not find this in any way elitist or discouraging as I believe that most undergraduate courses cover almost identical material in the first year.

Unparseable latex formula:

\rule[0.5ex]{\linewidth}{1pt}

Cambridge Part IA (schedule)
Lecture notes (IA Course notes)

Lecture notes from Cambridge
-Official lecture notes.

Lecture notes by 'Dexter Chua'.-At a glance seem very well-written and certainly up-to-date and relevant/useful.

Lecture notes from 'The Archimedeans' (Cambridge Mathematical Society).
-Whilst useful, many notes relate to the courses as taught many years ago.

Lecture notes by 'William Chen'.
-Not immediately relevant to the the specifics of the course, but seem a very accessible resource.

Lecture notes by 'Paul Taylor'
-Quite rather out-dated now, including this for completeness and because I think they're still interesting.

Lecture notes from other sources.
-This is essentially a catalogue of further reading recommendations and additional links to lecture notes.

Lecture notes and course materials from Oxford University.
-These look extremely good and also include problem sheets which would be particularly useful for those not going to Oxford.

MIT OCW Lecture course
-Whilst not directly synonymous to the Cambridge Tripos, it is nevertheless interesting and very useful.

Problems:

DPMMS Examples sheets from Cambridge
- Click on course name to access sheets. Would recommend against recent ones.

DAMTP Example sheets from Cambridge
- Would recommend against doing recent example sheets.

This thread
- I expect many people on this thread to share interesting questions and problems from a variety of sources for others to try.

Advanced integration techniques.
-Undoubtedly this will prove to be a favourite amongst those on this thread.

Selected problems, published by the Hong Kong mathematical society.
-This is an excellent resource.

Problems and solutions from miscellaneous competitions (Art of Problem Solving).
-Contains some gaps, but is a reliable source of diverse and irregular problems.

BMO and IMO.
-For the confident problem-solver.

'104 Number Theory Problems', from the training of the USA IMO team.
-Co-authored by 'Zuming Feng' should be all you need to know about why this is worth a read. The other books in there series are also very useful. For example: '103 Trigonometry Problems'.

STEP Mathematics.
-Arguably the best preparation for the types of problem-solving skills required for university. The 'Problem-Solving Society' is also a great resource.

'The Proof is Trivial'.
-An on-going problem-solving marathon packed with interesting and exciting problems (not limited to those listed in the O.P).

Calculus Challenge.
-Not as high a level as the majority of the problems you will find above but the papers make up a good resource for non-standard questions.

Introduction to Olympiad Inequalities, from the training of the Bangladeshi IMO team.
-I've read through several booklets on Inequalities and feel that this provides the most accessible introduction. It also places emphasis appropriately, which is always helpful for the problem-solver.

Courses

Michaelmas Term:

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Numbers and Sets:

Syllabus:

Syllabus



Book Recommendations:

Books



Problems and resources from this thread:

Problems



Unparseable latex formula:

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Groups:

Syllabus:

Groups Syllabus



Book recommendations:

Book Recommendations



Problems and resources from this thread:

Problems



Unparseable latex formula:

\rule[0.5ex]{\linewidth}{1pt}



Vectors and Matrices:

Syllabus:

Syllabus



Book recommendations:

Book Recommendations



Problems and resources from this thread:

Problems



Unparseable latex formula:

\rule[0.5ex]{\linewidth}{1pt}



[To add]

Miscellaneous Maths:

Spoiler


Good luck and have fun!
(edited 7 years ago)

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Reply 1
Avatar for Zacken
Zacken
OP
22
Reserved.
Reply 2
Avatar for Mop3476
Mop3476
1
Memes
Nice one, Z. :wink:
Original post by Zacken
Reserved.


Dropbox error on Feynman`s lectures on Physics :frown:.
dad
Original post by Kadak
Dropbox error on Feynman`s lectures on Physics :frown:.


they're also hostedo n caltech website as they 're public domain if you do a cheeky googleroo
Original post by Number Nine
they're also hostedo n caltech website as they 're public domain if you do a cheeky googleroo


Ty .
Reply 8
Avatar for Zacken
Zacken
OP
22
Original post by Kadak
Dropbox error on Feynman`s lectures on Physics :frown:.


Fixed, I think.
I live here now
Might as well sign in now...
:woo::woo::woo::woo:
(might as well decorate the place)
Hey lads. It's gonna be one great summer. :smile:
@Zacken, damn you put some real work into that OP.@Mathemagicien, @krishdesai7 here it is m8.
Thanks for this :biggrin:
Reply 15
Avatar for Zacken
Zacken
OP
22
Original post by Mathemagicien
Is there a limit to the length of posts?


Yes.
Original post by Insight314
@Zacken, damn you put some real work into that OP.@Mathemagicien, @krishdesai7 here it is m8.


Thanks.

Hallo everyone 😄
I read A Mathematician`s Apology a while ago,and while I did enjoy it,I still don`t get why it held in such reverence by pure mathematicians.
(edited 7 years ago)
First non mathmo, yesssssss
Original post by Zacken
Fixed, I think.


Thanks,for a bit of geopolitical balance how about adding a course of theoretical physics from Soviet physicist Lev Landau :tongue:!
https://archive.org/search.php?query=creator:%22L.D.+Landau+%26+E.M.+Lifshitz%22

By the way,do you have any resources on mathematical biology :smile:?

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