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25 Dec 2021Mathchan is launched into public
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File: Don't do it.jpg ( 39.73 KB , 720x890 , 1720789703734.jpg )

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  No. 863
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>>864 >>866 >>918
Hello everyone. I have seen a lot of threads(book threads, IMO advice...) that seem to exist solely so people give advice and give comments on your study material.
So I had an idea for a thread where we: state our goals, name the books(video series and other material) we plan to cover in a certain order, give an approximate deadline and other mathchan users can give suggestions, meaningful comments, advice and pointers to others!
I'll start:
My goal is to develop enough knowledge before I go to university where I hope to take advanced classes and spend more time on advanced topics while simultaneously getting myself ready for the national math competition(not my main focus, just for fun)
《Elementary math 1 i 2 notes》
-notes from my local university where they want to "bridge the gap between high-school and university math" (introductory logic, set theory, relations, functions, number theory, Euclidian geometry, vector spaces and analytic geometry)

《A Transition to Advanced Mathematics by Smith, Eggen, and St. Andre /// 101 problems in algebra》
-covers similair material as the already meantioned notes but in more detail

--------------I am here----------------

《Analysis I notes》
-notes from the local university, this time in calculus/analysis (what European universities call analysis is almost always just rigorous calculus or very elementary analysis since we cover calculus in HS)

《Linear Algebra Shilov》

《Šime Ungar, Analiza 3》
-same deal as before, rigorous calculus/ begginer analysis book for R^n

《101 problems in various topics, Andreescu books, generatingfunctionology, Problem solving strategies by Engels》

《Elements of Set Theory by Enderton》

《Introduction to Logic: and to the Methodology of Deductive Sciences by Alfred Tarski》

《An Introduction to the Theory of Numbers by Niven, Zuckerman, and Montgomery》
-mainly for competitive math but also as an introductory text

《The USSR olympiad problem book》

《Algebra by Artin》

《The Cauchy-Schwarz Master Class: An Introduction to the Art of Mathematical Inequalities by Steele》
-half for competitive maths, half since I heard analysis problems demand a lot of inequality knowledge

《Amann and Escher Analysis series》
-all three books

I hope to cover everything stated above in a 1.5-2 years. I covered the things above the "I'm here linePost too long. Click here to view the full text.
>>
  No. 864 >>901
>>863
Amann Escher do both analysis and calculus, so putting it at the end of your list isn't really ideal imo. Shilov has no prerequisites either. I'd recommend reading both earlier/now instead. The first chapter of Amann Escher is also a nice introduction to proof-based math in general.
For algebra, I read Gaitsgory's Math122 and Math123 notes (both are on AMS) combined with Lang's Algebra (didn't complete it though). Gaitsgory's notes on Math122 can also be used as a somewhat abstract course in linear algebra. I think he actually based his Math55a course on them, of which you can also find notes online. I also read the first few chapters of Gorodentsev but can't say much about it as I never finished it.
For Topology, I really like Brown's book "Topology and Groupoids". It has few prerequisites (if any) and is very interesting as it emphasizes applications in differential topology, algebraic topology and algebraic geometry (for instance, it introduces the Zariski topology early on in an exercise) whereas e.g. Munkres is far too focused on point-set topology, which you'll find in analysis books like Amann Escher anyway.
If you want a book that treats the differential geometry stuff in amann escher 3 in more detail, I recommend Sternberg's lectures on differential geometry. Kobayashi-Nomizu is the go-to book if you want to specialize in it (note that it'd most likely be a very difficult first read).
If you're interested in geometry I also highly recommend learning physics.
>>
  No. 866 >>901
>>863
i intend, wholely and fully, to have a good time
do tell if any of those problems are fun, i would be fine to check them out
>>
  No. 901 >>920
>>864
As you said, I am probably going to cover Amann and Escher quite a bit sooner. I think people scared me into thinking that analysis is more demanding than it probably is.
I also thought that set theory and logic are more basic in some sense than they are. But it seems to me like you only need basic logic (basic propositions, quantificators and so on) and just the very basics of set theory (sets, operations on sets, partitions and such) to cover math to a decently advanced level.

Thank you for the other recommendations as well.

>>866
101 problems in algebra I thought was okay. The difficulty of the problems differs quite a bit since I solved some in minutes and others left me confused even after checking the solutions.
Some of the explanations I didn't like at all. They don't explain the thought process and sometimes just begin the solution like this:

Since (critical part of the solution that greatly simplifies the problem) holds. We know that x is equivalent to y. Therefore z and therefore the statement is proved.
>>
  No. 918
>>863
A gentle intro will not be very beneficial and will waste time. The reason analysis is hard is because the ideas are presented in a way that is isolated and general. The same will go for algebra and topology. The books on those subjects should be read, but not be the center of your study. They are there for reference when needed.
I studied analysis and ignored everything else and it failed me. I then changed my approach, got a book on differential geometry (lee) and began to read that, referencing books on analysis, algebra, geometry and topology when it was necessary. Math is a slow process and the time you put in will significantly outweigh the knowledge you gain.
Also a little side note, get into complex analysis asap. Both (real and complex) deal with the same ideas, just complex analysis is more tangible due to its geometric nature. I recommend Ahlfors book.
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  No. 920
>>901
Logic and model theory are a bit weird in the sense that they're mostly disconnected from the rest of the math world despite seeming fundamental. Of course I am neither a logician or set theorist so my view may be biased but it is interesting how both camps often know very little about the other side. And then there's stuff like algebraic geometry in its formulation by grothendieck that seemingly required inventing/appealing grothendieck universes just to define some things rigorously. Turns out it wasn't necessary (see the stacks project, there's extensive discussion around size issues).

File: math_curriculum.png ( 1.12 MB , 1140x4777 , 1713088252224.png )

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  No. 688
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>>689 >>694 >>756 >>848 >>870
Please name all the books in picrel. Also review the curriculum shown. Are the books shown in the picrel enough to cover the mentioned topics. If so how long would it take.
31 posts and 3 image replies omitted. Click here to view.
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  No. 887 >>890
>>881
no dude the key is to just start as obvious as it may sound. If you want to do something, do it now.
I used to think I'd have no time to read during uni but that's all nonsense. Once I started doing my assignments immediately I had enough time to read through 4 books in one semester and that conversely helped me become really fucking good at math to the point of me going to far less lectures
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  No. 890 >>891
>>887
Did you do the exercises? Or only read those books. If yes then what percent of exercises like 50% or 80% or each and every one(skipping the trivial easy ones of course).
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  No. 891 >>892
>>890
Do all of them. When you get to my point in life where I've read one undergrad curriculum's worth of books, I can't remember what I need to any more. Burn it into your memory, because you can only ascend as strong as your foundation.
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  No. 892 >>919

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>>891
Can you specify which were those 4 books
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  No. 919
>>892
Federer. Geometric Measure Theory
Kashiwara. Sheaves on Manifolds
Harthshorne. Algebraic Geometry
Hotta. D-modules, Perverse Sheaves, and Representation Theory

File: 10FA814D-3F99-493D-B028-3E94484555B6.png ( 225.41 KB , 712x2584 , 1640980402330.png )

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  No. 91
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>>185 >>701 >>889
You can solve this, right?
3 posts and 2 image replies omitted. Click here to view.
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  No. 185
>>91
Yes. What's the time limit?
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  No. 700 >>703
Where is this an Enterance Exam to? I do not think I could do it. My undergraduate univeristy is all multiple choice and so I am nearly finished it having barely written a proof. It's awful.
>>
  No. 701
>>91
sneed
>>
  No. 703
>>700
I somewhat doubt it is an actual entrance exam. It reminds me of 1st year graduate course of mathematical methods in theoretical physics given that it has a bunch of maths without too much coherence.

Also, I think the ban on electronic calculators is quite futile here.
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  No. 889
>>91
the ideas here are easy but i don't know what C-convergence means
can someone link a book on the topic?

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  No. 878
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>>883
This is a thread to post a paper or book you are reading currently.
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  No. 879 >>884
i just started reading complex analysis of Stein & Shakarchi a few days ago. Currently on Cauchy's integral formula
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  No. 883

File: Elliptic Curves Lecture 5 - Isogeny.pdf ( 244.43 KB , 1721355587644.pdf )

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>>878
Right now I'm reading this series on Elliptic Curves. At the last lecture it gives an intelligible argument for Wiles' 5-3 trick.
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  No. 884 >>888
>>879
I like the way this is written. I may read this in the future since I haven't ever completed a book on Complex Analysis.
>>
  No. 888
>>884
Me too, i think its great at explaining things (although its stuff that i already know in the first chapters). I am a self studying 9th grader and ive also completed its Fourier analysis. I really love the way it teaches

File: 17014881352420.jpg ( 126.35 KB , 1488x1488 , 1716338431610.jpg )

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  No. 780
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>>782
do you look like a scientist?
>>
  No. 782 >>783
>>780
kill yourself 4cuck bhangi
>>
  No. 783
>>782
Man of cultutre right here
OP should live stream roping himself. Sage goes on all fields
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  No. 802 >>885
scientists look like that?
>>
  No. 885
>>802
only monkeys do but oh well
https://www.youtube.com/watch?v=6C-kBVggFrs

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  No. 559
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>>669 >>675 >>607 >>629 >>843
https://newsen.pku.edu.cn/PKUmedia/11888.html

>Of these 24 questions, Wei Dongyi completed 23 and a half, a record that even his coach was amazed by. He often solved all the questions in the first hour of the test. Many of the methods he used were self-invented and were much more concise than the standard processes, and became known as the "Wei Method".

>
In this competition, Wei beat the legendary Tao Zhexuan, who taught himself calculus at the age of seven and won the IMO gold medal at the age of 12, by a time ratio of 1:7. Tao Zhexuan was invited to solve the sixth problem of the finale, which took him seven hours, while Wei Dongyi took only one hour in the competition.

Is it really impossible to be like him with just learning and studying more? Is it really over, is only option actually suicide? Please be brutally honest, I don't want any false hope.(Even though I know the answer)
19 posts and 2 image replies omitted. Click here to view.
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  No. 675
>>559
its experience, solve more problems & learn more methods & you'll get better.
even if you don't its not the end of the world. you can still fuck women without being a three time IMO winner.
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  No. 805

File: a6ut63j7gaq41.png ( 248.8 KB , 880x620 , 1718071351919.png )

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>>608
Based low-iq proover ideology.
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  No. 817
>>630
Please specify what you have achieved
>>
  No. 843 >>844
>>559
test
>>
  No. 844
>>843
you realise you dont actually need to post to fill in the captchas right?

File: IMG_20220714_001733.jpg ( 5.31 KB , 240x60 , 1657768669674.jpg )

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  No. 236
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>>237 >>239 >>242 >>247 >>837
-1/12

contradiction or too complex for mere mortals to understand?
8 posts and 1 image reply omitted. Click here to view.
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  No. 304

File: merge_from_ofoct.jpg ( 799.81 KB , 951x6024 , 1663049911610.jpg )

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This physicist's treatment of the -1/12 issue from Zee's QFT book is the best treatment of the question I've seen.
>Appallingly, in an apparent attempt to make the subject appear even more mysterious than it is, some treatments simply assert that the sum is by some mathematical sleight-of-hand equal to -1/12. Even though it would have allowed us to wormhole from (1) to (3) instantly, this assertion is manifestly absurd. What we did here, however, makes physical sense.
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  No. 305
Behold, the Barnett-Tooker-Wildberger conjecture.

Let

ζ^b(s)=∑k=1∞^−bn−s\qquad \hat\zeta_b(s) = \sum_{k=1}^{\hat\infty - b} n^{-s}


then

ζ^e+π+2(−1)=eiπ11+0.999…\qquad \hat\zeta_{e + \pi + \sqrt 2}(-1) = \frac{e^{i\pi}}{11 + 0.999\dots}
>>
  No. 315
I still don't get it.
>>
  No. 811
Contraddiction, because in Ramanujan's proof there are mistakes i.e. the term equals zero changes the number of step in the serie and also it's true that
2>Σn=0+∞12n 2 > \Sigma_{n=0}^{+\infty} \frac{1}{2}^n
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  No. 837
>>236
it diverges up, right?
and the limit is the first value something dosent reach
therefore, the limit of the series must be down

File: yahtzee-chaos-1.png ( 2.41 MB , 1920x1080 , 1694700286881.png )

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  No. 499
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>>500 >>836
Mathematically speaking, what is the optimal strategy for yahtzee?
>>
  No. 500

File: yahtzee-chaos-2.png ( 2.08 MB , 1920x1080 , 1694701115191.png )

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>>499

We'll be playing yahtzee in vrchat this weekend.
  1. Free
  2. Linux-compatible
  3. No GPU required

People are smart
∩\cap
nice
∩\cap
cool. 33F6YsgTX8
>>
  No. 707 >>836

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Depends if the result is determined as a binary (or trinary) win/loss (+draw?) or if you're playing so that every point difference is $1 or something. Way easier to calculate if it's by point difference because then there's just a single, objective EV calculation and you don't even take the opponent's strategy into account, it can't change the EV of your own move.

If playing for a win and ignoring whether it's by 1 or 100 points, you get into obscene amounts of game theory, future game simulation and even psychological exploitation of mistakes (pointless to play if you're both optimal computers, so the mistakes will be there), and the game tree fucking explodes in complexity
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  No. 836
>>499
have fun?

money is a system of favors, and is as of such an inferior substitution to communal trust and direct manipulation, so even if you are betting like >>707 would imply, focussing on the people in the room is optimal

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  No. 769
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>>825 >>826
https://arxiv.org/abs/2405.03599

https://www.youtube.com/watch?v=1emC3ncjblU

https://people.mpim-bonn.mpg.de/gaitsgde/GLC/
>>
  No. 825
>>769
probably the most important proof this century
>>
  No. 826

File: 1718499390243213.png ( 166.13 KB , 1000x2000 , 1719251893933.png )

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>>769
Can you describe what are its implications

File: IMG_0671.jpeg ( 48.99 KB , 1230x324 , 1718303557158.jpeg )

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  No. 813
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The discrete logarithm
ax=b a^x=b
mod p is polynomial with a,p prime ≠ 2; the question is if a=2 or a is a dialed number is still polynomial? I troved a way, but is a class of solutions.

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