Άσχετο, αλλά θα συνέστηνα ανεπιφύλακτα αυτό το βιβλίο. Είναι πραγματικά fun και easy read - πάντα το διάβαζα στην τουαλέτα πριν την διάδοση των κινητών.
Άλλα δυστυχώς, δεν περιέχει την Σταθερά ΚΚΕ.
Evolution of numbers is the "basic story". This is what Einstein said about this book
"This is beyond doubt the most interesting book on the evolution of mathematics which has ever fallen into my hands. If people know how to treasure the truly good, this book will attain a lasting place in the literature of the world. The evolution of mathematical thought from the earliest times to the latest constructions is presented here with admirable consistency and originality and in a wonderfully lively style."
Read Amazon reviews to get more info.
Start here
Quadrivium: The Four Classical Liberal Arts of Number, Geometry, Music, & Cosmology (Wooden Books) https://www.amazon.com/dp/0802778135/ref=cm_sw_r_apan_glt_i_TEAWBZ5W4XRFZFRP8NWS
Read a book or 2
Quadrivium: The Four Classical Liberal Arts of Number, Geometry, Music, & Cosmology (Wooden Books) https://www.amazon.com/dp/0802778135/ref=cm_sw_r_apan_glt_i_EG6M2A4MYAZ9XSH390QX
PHILOMATH: The Geometric Unification of Science & Art Through Number https://www.amazon.com/dp/B093BC3K1X/ref=cm_sw_r_apan_glt_i_B92KRV9GWJK9ZCADRPCD
Only way to learn proofs is to do proofs. Look into induction, binomial theorem, even just start with something simple like prove sqrt(2) is irrational.
If you have Rogers buckle in for a wild ride. This is the book. Not a great book but it is a good list of topics.
https://www.amazon.com/Introduction-Mathematical-Reasoning-Numbers-Functions/dp/0521597188
Would easily be the best value for $35.33 you'd ever get. Pound-per-pound in terms of word economy, while giving mercy to let you get creative mathematically.
Can't remember much from my course, but going back through it, the first few chapters were fun. Doesn't make you fuck around with set theory notation beyond what is necessary and gets to the heart of what math is. Or at least shaped my understanding of it.
Will you know how to prove Green's theorem by the end of this book? No. Was the process of reading it an enlightening one for me, yes. To be fair, my course skipped some of the denser material, we definitely didn't cover prime numbers. Like I said, I don't remember everything that was covered, so if your hobby includes collecting wikipedia entries, count yourself out of this one or let it show you the futility in that endeavor.
That said, if a function based understanding of calculus is what you desire, there is merit in that path as well. I found differential equations to be very rewarding, but it's been years since I learned it so I can't even tell you what a differential equation is.
Sadly I have no use for my copy anymore. If anyone wants it, I'll even buy the flat-rate shipping box. But then I know your address. I'll put mine on there too. :)
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Seriously, if you can buy it on amazon instead, lol.
The book Quadrivium is great, it explains the maths behind melody and harmony. Its a great read, you should check it https://www.amazon.com/Quadrivium-Classical-Liberal-Geometry-Cosmology/dp/0802778135
"Numerical Analysis", 7th ed, Richard L. Burden and J. Douglas Faires. Link: https://www.amazon.com/Numerical-Analysis-Richard-L-Burden/dp/0534382169/ref=sr_1_3?ie=UTF8&qid=1475930798&sr=8-3&keywords=numerical+analysis+burden used this as a reference for researching/working with professor
Nice, I'll have to check that out.
The Quadrivium has a lot of this cosmic coincidence / geometric correlations as well.
And there's always A little book of coincidence in the solar system
Like /u/wygibmer said, check out Project Euler. Most of the problems are conceptually pretty easy, so you get to consider how to create and implement algorithms to problems without having to worry about super complicated solutions.
But really, the thing that got me started was a course called "Mathematical methods for chemical engineers".
If you're looking for a formal approach, we used a textbook that was ok.
I found a PDF of it somewhere if you don't want to buy it.
Beyond assigned college textbooks, the book that influenced me the most and prepared me for higher mathematics was "An Introduction to Mathematical Reasoning" by Ecceles:
http://www.amazon.com/Introduction-Mathematical-Reasoning-Peter-Eccles/dp/0521597188
It starts off simple that any high school student can understand and go through in topics that are somewhat familiar or at least easy to grasp. The beauty comes from doing the problems at the end of each section. A lot of them are easy to understand and accept, proving them is a bit challenging.
I learned the basics from Peter Eccles's An Introduction to Mathematical Reasoning. The primary focus of the book is on proof techniques, not set theory, but I think it presents the very basics of sets and functions in a nice cohesive way. I recommend it as both a very basic introduction to sets and as good preparation for upper division proof based math classes you will probably start taking soon.
If you are looking for a more advanced reference I would recommend going to your university library, finding the section where the algebra and set theory books are and just check a bunch of them out. Try reading each of them and return the ones you don't like. Rinse and repeat until you find one that clicks with you.
Check your pm in a lil...I'll share it with ya via dropbox or something. It's on my laptop but I'm on my phone. You don't want to buy the book...it's like $300
edit: k so i was wrong, it's only $95 lol. I'll still share the pdf with you if you're curious
Numerical and Analytical Methods with MATLAB (Computational Mechanics and Applied Analysis) https://www.amazon.com/dp/1420093568/ref=cm_sw_r_awd_X2q6ub1G01G99
The Music of the Primes is my favourite book about mathematics. It tells a history of the study of prime numbers, important contributions, and open problems.
Uncle Petros and Goldbach's Conjecture is a work of fiction. It gives an insight into the mind of a genous, who becomes obsessed and begins to unravel.
I will second Godel Escher Bach: An Eternal Golden Braid as jeff0 suggested. This is probably my all time favourite book. It's a book about the incompleteness theorem, and its connections to computer science, consiousness, and philosophy of mind. It's written in a beautiful manner, divided into "preludes" and "fugues" (in the style of Bach's compositions). The preludes are short "plays" where the characters, topics, and structure echos the ideas discussed in the following (fugue) chapter.
Last I want to unsuggest Flatland, which thenumber0 suggested. I found it to be a great idea, but an awfully boring book. I found the victorian writing tedious and irrelevant. The amount of discussion on the social hierarchy of the geometric shapes, with women (line segments) at the bottom of course, was almost unbearable. There are some modern animated versions which I'd suggest instead.
if you spend time studying liberal arts and sciences you should pick up this book as well. I work as an artist (music and different forms of flow and object manipulation), and I'm starting my own company to sell LED flow toys to others with the addition of a section educating people on how to use them. if you're into that type of thing, or just want to learn more about the world around us, it will be a great read for you. i actually own 3 copies cause it's so cheap so i loan two out at a time to my friends :) http://www.amazon.com/Quadrivium-Classical-Liberal-Geometry-Cosmology/dp/0802778135
I would recommend geometry or number theory.
Also, not a text book, but definitely made me excited about maths and at the time I read it, Music of the Primes - Marcus du Sautoy. It's a very accessible and well written book about the Riemann Hypothesis.
It would be helpful to know what your background is to recommend a suitable text.
The class I took "Math Reasoning", which I believe is equivalent to the one you're taking used this book. www.amazon.com/Introduction-Mathematical-Reasoning-Peter-Eccles/dp/0521597188/.
I cannot, however, give you any advice on how it compares to your book, as I'm not familiar with yours.
What about Number: The Language of Science by Tobias Dantzig? I came across it at a Border's closing and rather enjoyed it.
The Music of the Primes: Searching to Solve the Greatest Mystery in Mathematics by Marcus du Sautoy - A historical account about the development of the Riemann Hypothesis.
I am not sure what kind of 'basic mathematics' you are looking for, but I can recommend this book which teaches you to think mathematically - how to read and understand math problems, formulate proofs (properly), and teaching you the basics of number theory.
The Penguin Dictionary of Curious and Interesting Numbers
There is a matching "Curious and Interesting Geometry" which I like even better, but it seems difficult to find at a sensible price.
What's with the downvotes? This is a modern continuation of the classic tradition of finding interesting facts about numbers, which would not be out of place in the Penguin Book of Curious and Interesting Numbers - although it might need some explanation of the meaning of both 1337 and 42, which may be the problem here.