Ambitious, probably delusional guy wants to make a Kiselev manual

In summary, an ambitious individual has a goal of creating a Kiselev manual, but this may be a delusional aspiration. The manual would likely be based on the teachings of Russian mathematician and educator, G. Kiselev.
  • #1
SomeGuyLearningMath
How did you find PF?
Searching for book recommendations on DDG and landed here.
Nice to meet you all!

I am a college dropout self-studying math. Before dropping out, I flunked out my Calculus class even though I managed to pass my Precalculus class (I honestly don't know how). I realized that I was lacking a lot in Geometry and Trigonometry. My understanding of algebra is quite average, but I am very unsatisfied with it after seeing Euler's Algebra and Introductio in Analysin Infinitorum.

I realized how disappointed I am at my mathematical upbringing. Math education is practically non-existent in my country - I was able to pass through high school without knowing the notions (even the words themselves!) of congruence, similarity, induction, and other basic stuff. The only mathematicians I knew were literally only Euclid, Descartes, Newton, and Leibniz - Newton being a miracle genius that invented the entirety of modern science and calculus after an apple fell into his head; and Euclid, Descartes, and Leibniz being footnotes at my textbooks.

I have also seen how math people talk so enthusiastically even with smallest of the minor stuff like the textbook they use at class (e.g. Spivak, Hubbard & Hubbard, Arnold), and how enthusiastically they talk about solving hard problems (e.g. problems on a textbook for math circles) and seeing the beauty and unity of mathematics for themselves (e.g. how Euler's Formula reveals the unity of algebra, geometry, trigonometry, and complex numbers). I also became aware of the lives of mathematicians with Posamentier's Math Makers, Hoffman's The Man Who Loved Only Numbers, and Kanigel's The Man Who Knew Infinity. I realized that mathematicians are not just introverted geniuses that write equations no one else understands on blackboards. I became very intrigued and curious about mathematics in the last few months.

I am coming back to college this year or next year (depending on circumstances) to study for another degree, but I want to get my hands dirty with mathematics. I am planning to study Elementary Mathematics again (since I have a lot of time in my disposal in the coming months), but this time in a serious manner - without the frills of the education system, using the following books:
  • Some parts of Elementary Algebra (Chrystal) - 2 Volumes
  • Numbers and Geometry (Stillwell)
  • Planimetry and Stereometry (Kiselev, Givental)
  • Trigonometry (Gelfand, Saul)
I will definitely struggle reading the following books and not be able to read them on my own. I am also planning to compile solutions to some exercises on the two books by Kiselev. I am not yet sure whether I'll be able to do this or not since it seems to be a humongous and arduous task (probably too ambitious also) - but still, I genuinely want to try. The books seems to be outstanding considering its history - it probably taught a lot of great mathematicians considering its wide usage in Asia and Europe before. I believe it will be a great book for people who looks for serious business when it comes to studying geometry and math in general. Its only drawback is the lack of a solutions manual. I know that there are numerous ways one can prove a mathematical proposition (e.g the Pythagorean Theorem has hundreds of different proofs) and this fact is being obscured by the plug-and-chug nature of the education system; but I believe that a solutions manual can be an invaluable resource for people who will read or teach using the textbooks.

I will be posting here my learning journey soon- what I've learned, questions, struggles, etc. I also want to generate discussions regarding the stuff that I will read. I'll probably also post a Github repository of the latex files of the solutions manual soon. This community at glance seems to be very bright, vibrant, and helpful; and I hope to talk with you all! Again, nice to meet you all and let's do math together!
 
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  • #2
:welcome:
 
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  • #3
Welcome to PF. :smile:

SomeGuyLearningMath said:
I am planning to study Elementary Mathematics again

When you get stuck on a problem, start a thread in the Homework Help, Pre-Calculus Math forum. Provide the problem statement and any relevant equations, and then show your best efforts to work on the problem. You will get good help here with such thread starts.

It sounds like you are already familiar with LaTeX, which is great. Maybe skim the "LaTeX Guide" link below the Edit window to look for any variations in LaTeX that the PF implementation may have.

Enjoy PF! :smile:
 

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