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Mathematics Study & Teaching books:
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Top Reddit reviews mentioning Mathematics Study & Teaching books:
you should definitely give harder problems multiple tries, you might not be able to solve them right away. Go back and re-learn the concepts the problem needed. Sometimes you might need to use a concept which you are not familiar with at the moment. I recommend reading "How to Solve it " by G. Polya https://www.amazon.com/How-Solve-Mathematical-Princeton-Science/dp/069116407X
It covers different problem solving approaches in a agnostic fashion.
I used to be a dealer too! I ended up dealing blackjack, roulette, craps, bacc, Pai Gow, and many poker variants. I recommend that you read the book Secrets of Mental Math or watch the dvd. To practice, look at getting an app called Anki and make flashcards for yourself. Good luck and have fun!
Hi. I really enjoy this book. I say in present tense as I often go back: "Mathematics: From the Birth of Numbers" by Jan Gullberg. The author wrote the book for the benefit of his son who was entering an academic program. He wanted something that encompassed math technique and history. It is a brilliant work. It wont be your only stop but it is a great map of the concepts up to and lightly into calculus. This history may help you connect to the technical aspects. https://www.amazon.com/Mathematics-Birth-Numbers-Jan-Gullberg/dp/039304002X.
Best of luck.
A PhD is Not Enough! A Guide to Survival in Science by Peter J. Feibelman Amazon link
Make Your Mark in Science: Creativity, Presenting, Publishing, and Patents, A Guide for Young Scientists by Claus Ascheron and Angela Kikuth Amazon link
Hey! Fellow sellout here.
I don't want to gloss over the fact that it's a massive lift, but I'm about 100 pages into the Princeton Companion (https://smile.amazon.com/dp/0691118809/ref=cm_sw_r_cp_apa_glt_fabc_BMQ2QH2XA4C6B34M130J) and I personally love it. It's extremely well cross referenced so you do not need to read it cover-to-cover.
I love it because it gives just enough depth for you to get an intuitive flavor of different topics and areas. It tells me just enough, without pulling punches, for me to tell if a topic is something I want to look more into and in a serious way.
I had a similar request to yours, except I wanted to go beyond Calculus to get a broad survey of mathematical topics, using a ground up approach. The Princeton Companion to Mathematics is exceptional, I can't recommend it enough! It covers all the topics you wish your mathematics teachers had instilled in you, all within a comprehensive & comprehensible form. It has been years since I studied math. I've long since forgotten a majority of what I was taught but, I can still easily progress in this book and I feel like I finally understand many of the ideas that were impenetrable before.
I'm not alone in my positive review. You'll note that people have been heaping praise onto this volume on Amazon and in more formal book reviews as well.
I read this about a year into grad school (previous version). It's got some good general advice on how to think about your time and what to do with it to succeed.
https://www.amazon.com/PhD-Not-Enough-Survival-Science/dp/0465022227
Don't walk, run to the....cartoon guide to stats. No joke! Saved my bacon in grad school. Not sure how it will look as a sited work.
I second the Companion. It's $63 new on Amazon, and reading it has given me a much broader understanding of modern math.
I would say start with learning how proofs work. They can sometimes be confusing at first and (in my experience at least) calc doesn't do a great job of explaining them.
I learned from a book called A Transition to Advanced Mathematics it's been around for years, I know you can find copies of it for ~$5 without much trouble. It's got a good introduction to basic proof structure and ideas as well as dipping it's toes into combinatorics, algebra, analysis, and topology.
Another book worth looking into might be Book of Proof I personally don't have much background with this book, but it's the one used by my old university for their introductory course to proofs.
statistics is magic for muggles :)
i've really enjoyed reading some of the "cartoon guide" series. Here's a link to the one on stats:
https://www.amazon.com/Cartoon-Guide-Statistics-Larry-Gonick/dp/0062731025
It's true, I'm currently self studying and I understand everything 10x better. I use this book: (No Bullsh*t guide to math - Ivan Savov)
https://www.amazon.com/No-bullshit-guide-math-physics/dp/0992001005
Well... if you're not a trained mathematician at a PhD level with years of research, I don't think those problems are worth your time.
You can always try problems that are close to your level. You don't have to take on fights you'll probably lose. There are many problem books to sharpen your math skills and have some good time. For example:
https://www.amazon.com/USSR-Olympiad-Problem-Book-Mathematics/dp/0486277097
Academic side of academia? Not sure what that means, but it sounds like an unhealthy reason to do a PhD, FWIW.
If you're serious about finding your way in academia, I recommend the book <em>A PhD Is Not Enough!</em>
The Cartoon Guide to Statistics is a little cheesy, but might be helpful as you think of ways to translate technical information to non-technical audiences.
I liked this book when I was younger: https://www.amazon.com/Transition-Advanced-Mathematics-Douglas-Smith/dp/0495562025. It will help him make the jump from what's typically available in high school to what he'll encounter later. People are recommending Spivak's calculus, which is awesome, but I'm glad I had the one I linked under my belt before reading Spivak.
There is a whole series of Manga science books that might interest your students. For example The Manga Guide to Physics, The Manga Guide to Biology. You can order them from Amazon. https://www.amazon.com/Manga-Guide-Calculus-Hiroyuki-Kojima/dp/1593271948/ref=sr_1_5?keywords=manga+physics&qid=1639271562&sr=8-5
Not knowing anything about your background, I would recommend this book as a place to start. $12 from Amazon. Most stat books can be a little dry ...
The book that was used in my Intro to Proofs course was A Transition to Advanced Mathematics by Smith, Eggen, and St. Andre. Maybe the difference in presentation will make things click, but what I think might help better is a course or lecture series - like this for example. Both Book of Proof and the textbook I used start from what I'd call the basics - sets and propositional logic. Most textbooks will.
You might also want to look into materials for Discrete math courses. These tend to be courses mainly going over logic and sets, and are what a lot of students take before their Intro to Proofs course. That extra focus on those topics may be what you're missing.
In addition to the other comments, read A PhD is not Enough!.
How to Solve it: A New Aspect of Mathematical Method
https://www.amazon.de/dp/069116407X?linkCode=gs2&tag=uuid0a-21 (kindle verson ~14€)
idk, you might find it for free somewhere on the internet but i bought it. its absolultely worth its money
I suggest the book
"The cartoon guide to statistics".
https://www.amazon.com/dp/0062731025/ref=cm_sw_r_cp_awdb_imm_FMKDXA7W4M9P6RTX69R1
It follows the same format as intro stat books but it's actually fun to read.
It is my optional book for my stats students. if you try, you can get a PDF of it online for free.
Oh wow, I've never actually talked with anyone who shared that experience. It certainly is really frustrating. Meds don't really help with it, either, even though they've made a huge difference for me in other areas.
I did get a book that improved my mental math a bit, since it taught me new methods that I wasn't aware of. It doesn't help with holding the numbers in my head, but I'm still glad I read the first quarter or so of it. Here's a link:
Also on Amazon - https://www.amazon.com/Manga-Guide-Calculus-Hiroyuki-Kojima/dp/1593271948 but buying a ebook direct from No Starch Press gets you a version without any DRM.
Once you are ready to get into calc, Apex calculus is a great free online textbook. Also, if you are looking for a real book, “Mathematics: From the birth of numbers” by Jan Gullberg is very interesting (it becomes more of an encyclopedia near the end though)
Mathematicians strive to arrive at a deduction before they publish. But the “doing of mathematics” is not deductive. See e.g. How to Solve It.