Reddit mentions: The best elemetary mathematics books

This is a compilation of what I gathered from reading on the internet about self-learning higher maths, I haven't come close to reading all this books or watching all this lectures, still I hope it helps you.

General Stuff:
The books here deal with large parts of mathematics and are good to guide you through it all, but I recommend supplementing them with other books.

1. Mathematics: A very Short Introduction : A very good book, but also very short book about mathematics by Timothy Gowers, a Field medalist and overall awesome guy, gives you a feelling for what math is all about.
   
   
2. Concepts of Modern Mathematics: A really interesting book by Ian Stewart, it has more topics than the last book, it is also bigger though less formal than Gower's book. A gem.
   
   
3. What is Mathematics?: A classic that has aged well, it's more textbook like compared to the others, which is good because the best way to learn mathematics is by doing it. Read it.
   
   
4. An Infinitely Large Napkin: This is the most modern book in this list, it delves into a huge number of areas in mathematics and I don't think it should be read as a standalone, rather it should guide you through your studies.
   
   
5. The Princeton Companion to Mathematics: A humongous book detailing many areas of mathematics, its history and some interesting essays. Another book that should be read through your life.
   
   
6. Mathematical Discussions: Gowers taking a look at many interesting points along some mathematical fields.
   
   
7. Technion Linear Algebra Course - The first 14 lectures: Gets you wet in a few branches of maths.
   
   Linear Algebra: An extremelly versatile branch of Mathematics that can be applied to almost anything, also the first "real math" class in most universities.
   
   
8. Linear Algebra Done Right: A pretty nice book to learn from, not as computational heavy as other Linear Algebra texts.
   
   
9. Linear Algebra: A book with a rather different approach compared to LADR, if you have time it would be interesting to use both. Also it delves into more topics than LADR.
   
   
10. Calculus Vol II : Apostols' beautiful book, deals with a lot of lin algebra and complements the other 2 books by having many exercises. Also it doubles as a advanced calculus book.
    
    
11. Khan Academy: Has a nice beginning LinAlg course.
    
    
12. Technion Linear Algebra Course: A really good linear algebra course, teaches it in a marvelous mathy way, instead of the engineering-driven things you find online.
    
    
13. 3Blue1Brown's Essence of Linear Algebra: Extra material, useful to get more intuition, beautifully done.
    
    Calculus: The first mathematics course in most Colleges, deals with how functions change and has many applications, besides it's a doorway to Analysis.
    
    
14. Calculus: Tom Apostol's Calculus is a rigor-heavy book with an unorthodox order of topics and many exercises, so it is a baptism by fire. Really worth it if you have the time and energy to finish. It covers single variable and some multi-variable.
    
    
15. Calculus: Spivak's Calculus is also rigor-heavy by Calculus books standards, also worth it.
    
    
16. Calculus Vol II : Apostols' beautiful book, deals with many topics, finishing up the multivariable part, teaching a bunch of linalg and adding probability to the mix in the end.
    
    
17. MIT OCW: Many good lectures, including one course on single variable and another in multivariable calculus.
    
    Real Analysis: More formalized calculus and math in general, one of the building blocks of modern mathematics.
    
    
18. Principle of Mathematical Analysis: Rudin's classic, still used by many. Has pretty much everything you will need to dive in.
    
    
19. Analysis I and Analysis II: Two marvelous books by Terence Tao, more problem-solving oriented.
    
    
20. Harvey Mudd's Analysis lectures: Some of the few lectures on Real Analysis you can find online.
    
    Abstract Algebra: One of the most important, and in my opinion fun, subjects in mathematics. Deals with algebraic structures, which are roughly sets with operations and properties of this operations.
    
    
21. Abstract Algebra: Dummit and Foote's book, recommended by many and used in lots of courses, is pretty much an encyclopedia, containing many facts and theorems about structures.
    
    
22. Harvard's Abstract Algebra Course: A great course on Abstract Algebra that uses D&F as its textbook, really worth your time.
    
    
23. Algebra: Chapter 0: I haven't used this book yet, though from what I gathered it is both a category theory book and an Algebra book, or rather it is a very different way of teaching Algebra. Many say it's worth it, others (half-jokingly I guess?) accuse it of being abstract nonsense. Probably better used after learning from the D&F and Harvard's course.
    
    There are many other beautiful fields in math full of online resources, like Number Theory and Combinatorics, that I would like to put recommendations here, but it is quite late where I live and I learned those in weirder ways (through olympiad classes and problems), so I don't think I can help you with them, still you should do some research on this sub to get good recommendations on this topics and use the General books as guides.

There would have been a time that I would have suggested getting a curriculum
text book and going through that, but if you're doing this for independent work
I wouldn't really suggest that as the odds are you're not going to be using a
very good source.

Going on the typical

Arithmetic > Algebra > Calculus

****

Arithmetic

Arithmetic refresher. Lots of stuff in here - not easy.


I think you'd be set after this really. It's a pretty terse text in general.

*****

Algebra

Algebra by Chrystal Part I

Algebra by Chrystal Part II

You can get both of these algebra texts online easily and freely from the search

chrystal algebra part I filetype:pdf

chrystal algebra part II filetype:pdf

I think that you could get the first (arithmetic) text as well, personally I
prefer having actual books for working. They're also valuable for future
reference. This filetype:pdf search should be remembered and used liberally
for finding things such as worksheets etc (eg trigonometry worksheet<br /> filetype:pdf for a search...).

Algebra by Gelfland

No where near as comprehensive as chrystals algebra, but interesting and well
written questions (search for 'correspondence series' by Gelfand).

Calculus

Calculus made easy - Thompson

This text is really good imo, there's little rigor in it but for getting a
handle on things and bashing through a few practical problems it's pretty
decent. It's all single variable. If you've done the algebra and stuff before
this then this book would be easy.

Pauls Online Notes (Calculus)

These are just a solid set of Calculus notes, there're lots of examples to work
through which is good. These go through calc I, II, III... So a bit further than
you've asked (I'm not sure why you state up to calc II but ok).

Spivak - Calculus

If you've gone through Chrystals algebra then you'll be used to a formal
approach. This text is only single variable calculus (so that might be calc I
and II in most places I think, ? ) but it's extremely well written and often
touted as one of the best Calculus books written. It's very pure, where as
something like Stewart has a more applied emphasis.

**

Geometry

I've got given any geometry sources, I'm not too sure of the best source for
this or (to be honest) if you really need it for the above. If someone has
good geometry then they're certainly better off, many proofs are given
gemetrically as well and having an intuition for these things is only going to
be good. But I think you can get through without a formal course on it.... I'm
not confident suggesting things on it though, so I'll leave it to others. Just
thought I'd mention it.

****

It's a pretty difficult question to answer because only you know what you want out of this (or maybe, you don't know yourself!)

"I want to see what kind of mathematics is out there"

Try The Joy Of X. This is a super fun "guided tour" of mathematics. Each chapter surveys a different mathematical topic with examples, intutions, and fun thought experiments. You won't learn to "do the math", but you should have more of an idea of the kinds of things mathematicians think about, and some of the history of mathematics. This is easy and enjoyable, even though no mathematical background.

There's a "Hard mode" version of this called Concepts Of Modern Mathematics. The language is still light and informal, but the concepts are dealt with in more depth and abstraction -- there are fewer "real life" examples, and you will have to follow some real mathematical arguments in your head or on paper. This is more difficult, but still requires no formal mathematical background.

The other place to check of course is YouTube. 3Blue1Brown, Mathologer, Numberphile and many other channels have great exposés of mathematical concepts for the general audience, with 3Blue1Brown being my favourite for his wonderful animations.

"I want to actually improve my mathematical knowledge and skill"

This is difficult, but doable. I'm a mature mathematics student, and I was only really in with a shot of university owing to the kindness of my then fiancée supporting me while I knuckled down and learned the basics. The first step will be to brush up on what you should know from school. I'm not really sure what to recommend here; most texts targeted at this level of mathematics are targeted at... well, bored teenagers who don't want to learn mathematics, rather than keen adults possessing of some degree of patience and perseverance. I suppose Serge Lang, probably the most prolific mathematics textbook author of all time, can offer "Basic Mathematics", but this means paying Springer textbook prices, unless you enjoy marauding on the high seas. Khan Academy is a website with dozens (hundreds?) of free videos, articles, and exercises on basic mathematics

After you're up to speed on your basic algebra and geometry, the two most widely applied and important topics in mathematics beyond school-level are calculus and linear algebra (other than maybe statistics and probability). Calculus is typically learned first, but actually, it doesn't really matter which order you do these in. Exactly how to learn these topics is also a pretty difficult question, and depends what you want to get out of it. I guess post back here if "step 1" (recovering all your school-level maths) goes well?

Maths is hard, but fun. You have to do exercises and practice. You have to think deeply about difficult and abstract concepts. If you do choose the "improve actual skill" route, I'd still recommend supplementing your learning with the books and YouTube videos from the first half of this reply. Being exposed to fun new ideas regularly helps motivate you to push through the technical difficulties of learning it "properly".

I don't know what's going on in this thread. One poster is giving you useless advice about just "trying hard and keeping at it" (as if that's at the root of this issue), one poster saw an opportunity to vent about his personal frustrations and project them onto you (your supervisors are tools, they only care about promotions!), and yet another one decided to pitch in with a useless comment about some random exam they have tomorrow.

So let me give you a level-headed comment that might actually prove useful to you.

First off, you took zero math courses during your undergrad. There's your first problem. Geophysics is what happens when the concept of an inverse problem takes on the shape of an academic discipline. It's a very mathematical and physical subject.

Ideally, you should have completed all of single- and multi-variable calculus. You should have completed a course in linear algebra. You should have completed a course on differential equations (both ordinary and partial), and you should have a solid "signals and systems" course under your belt. Additionally, it'd be very useful if you had a (mathematically-oriented) course on probability and statistics, though this isn't strictly necessary at all, the preceding courses should suffice for 95% of the stuff you need to know.

That about concludes the mathematical side of things. Now let's be real. I just listed about 2 years worth of mathematical coursework, split over at least 5 quarter or semester courses. You're not going to be able to catch up with that.

My solution: get a "Mathematical Methods for Physics/Engineering"-style textbook. There's a few on the market, such as Boas' famous book. That one doesn't start at your current level though, so I don't recommend purchasing it.

The one book that fits the bill for you, and that I'd strongly recommend you purchase is Riley, Hobson and Bence's "Mathematical Methods for Physics and Engineering", Cambridge University Press. Get the latest edition (the 3rd). If you're in the US, the book will set you back about $60 on Amazon, or $50 on Bookdepository. Don't buy the cheap, crappy international edition. This book is massive (1300+ pages). Skip the chapters on quantum operators, group theory and representation theory. Work through the rest. Alternatively, an equally good book, though more concise, is "Mathematical Methods for Physics and Engineering", the 2nd edition by Weltner, Weber and other authors (it's a Springer book). This one really builds you up from scratch, which is great for a beginner like yourself, but hardly has any exercises. If you're really, really short on time, get Weltner et al. If you think you can put in the work and time, definitely go for the Riley/Hobson/Bence book. Also, definitely think about getting a Schaum Outline on Precalculus to quickly get up to speed on some fundamentals (a physical copy will only set you back $14 on Amazon). Seriously, this might prove very useful to you. Don't get the e-book editions,though. They're badly formatted.

That's at least 1000 pages of dense mathematics. If you're confident you're determined enough to get through it, that should be a good stepping stone to start from.

Next up is the physics. Get a University Physics textbook. I'm a big fan of Young and Freedman's University Physics, though you could consider Manfield's Understanding Physics as well as it might be more accessible to you. Study through the sections on mechanics (statics, dynamics, mechanics of materials), electromagnetism and waves (especially the waves section).

At this point you should really consider getting up to speed on signals and systems. Especially seeing as you're working with stuff like SEISAN (which is basically applied signals & systems theory). The one book that stands out, big time, is Lathi's "Linear Systems and Signals, 3rd edition". This text is amazing for self-study. It's incredibly expensive though. If you can't spare the money, there's a pretty cool little book that's freely available and unlicensed, written by prof. Chi-Tsong Chen from Stony Brooks. You will find it here, titled Signals & Systems: a Fresh Look. It even has a brief section on seismometers.

From here on out, ask your supervisors etc what books they'd suggest that specifically deal with geophysics/seismic stuff. I could recommend you a few if you're still interested after reading this daunting wall of text.

Let me know!

I did LA to Chicago. It was more to get from Point A to Point B than for sightseeing and we had a U-Haul trailer, so we did it in 3-4 days. But here are some pointers that may apply to you.

• I can't advise on national parks since I've never been to many, but I hear Bryce Canyon and Arches are amazing, or Glacier and Yellowstone if you're taking a northern route. I have been to Joshua Tree and highly recommend it especially if you like rock climbing/free climbing and weird fuzzy alien trees. I also liked Boulder, CO - fun uni town with a gorgeous range of mountains in the background.
  
  
• Going over the Grapevine into Southern California, be prepared to roast in your car. Because of the high desert temperatures and the steep grade of the road, it's easy for your engine to overheat and there are signs to turn off your air conditioner. I've seen a few cars pulled over with the hood up and the engine smoking on that stretch.
  
  
• If you're taking an extremely southern route then you don't have to worry about this, but most likely you'll be going through the Rockies. Look up some info/tips on crossing mountains because temperatures can drop pretty quickly and you should have proper supplies with you. In any case it's a good idea to have extra water & food, spare tire and jack, first aid kit, road flare, blanket, snow scraper etc. I wouldn't rely entirely on a cell phone because reception can be spotty.
  
  
• If you see signs for "Next gas station [large number of] miles", take them seriously and don't be afraid to turn around for gas. Especially in the Kansas/Nebraska/Wyoming area.
  
  
• There's a book called "Weird U.S." that lists quirky out-of-the-way spots.
  
  
• In the large cities like LA & NY, pubs and bars sometimes won't accept an out-of-state driver's license if you look young so it helps to have your passport handy. On the other hand, those are the places where it's most likely to get lost/stolen so you'll have to weigh the risks. It's not like the UK where you only need ID to get a drink (if even that) - a lot of times they won't even let you in the door without one.
  
  I lived in LA for a long time so if you want specific recommendations for places to eat and things to do there, let me know :)

This is just my perspective, but . . .

I think there are two separate concerns here: 1) the "process" of mathematics, or mathematical thinking; and 2) specific mathematical systems which are fundamental and help frame much of the world of mathematics.

​

Abstract algebra is one of those specific mathematical systems, and is very important to understand in order to really understand things like analysis (e.g. the real numbers are a field), linear algebra (e.g. vector spaces), topology (e.g. the fundamental group), etc.

​

I'd recommend these books, which are for the most part short and easy to read, on mathematical thinking:

​

How to Solve It, Polya ( https://www.amazon.com/How-Solve-Mathematical-Princeton-Science/dp/069111966X ) covers basic strategies for problem solving in mathematics

Mathematics and Plausible Reasoning Vol 1 & 2, Polya ( https://www.amazon.com/Mathematics-Plausible-Reasoning-Induction-Analogy/dp/0691025096 ) does a great job of teaching you how to find/frame good mathematical conjectures that you can then attempt to prove or disprove.

Mathematical Proof, Chartrand ( https://www.amazon.com/Mathematical-Proofs-Transition-Advanced-Mathematics/dp/0321797094 ) does a good job of teaching how to prove mathematical conjectures.

​

As for really understanding the foundations of modern mathematics, I would start with Concepts of Modern Mathematics by Ian Steward ( https://www.amazon.com/Concepts-Modern-Mathematics-Dover-Books/dp/0486284247 ) . It will help conceptually relate the major branches of modern mathematics and build the motivation and intuition of the ideas behind these branches.

​

Abstract algebra and analysis are very fundamental to mathematics. There are books on each that I found gave a good conceptual introduction as well as still provided rigor (sometimes at the expense of full coverage of the topics). They are:

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A Book of Abstract Algebra, Pinter ( https://www.amazon.com/Book-Abstract-Algebra-Second-Mathematics/dp/0486474178 )

​

Understanding Analysis, Abbott ( https://www.amazon.com/Understanding-Analysis-Undergraduate-Texts-Mathematics/dp/1493927116 ).

​

If you read through these books in the order listed here, it might provide you with that level of understanding of mathematics you talked about.

This was the book I used in my precalc class and I thought it was pretty good. There are only three chapters which really focus on trig (4: traditional 5: analytical 6: additional) which you can skip but I'd recommend tackling chapter five as it is based on trig identities and and has you prove things which is useful to change up the pace and for later classes. Chapter six also has vectors which is super useful in later courses (Calc, LINEAR ALGEBRA, physics, etc.).

The rest of the book is pretty great. It starts out kind of boring (focusing a lot on functions) but from what I remember, the "new" concepts really start at chapter five (I might be wrong so look over the earlier chapters to make sure you know what they're talking about). You must NOT SKIP CHAPTER 7&8 as they form the foundation for linear algebra (considered Calc 3 at my school). I'm also pretty sure that chapters 9 and 10 are covered more in depth in Calc 2 so I'd recommend doing these as well. There's also an introduction to limits but we didn't get that far in the book so I don't know how "good" that section is.

Also, I got the chapter names and topics from Slader which covers this book: http://www.slader.com/textbook/9780618660896-larson-precalculus-with-limits/

Khan Academy is good for everything. Loads and loads of videos and tutorials if you're willing to put the time into them. I learned some stuff from here.

MIT Lectures are also great. I watched numerous of these and they're a great resource.

Since I'm in electrical engineering, I got Electronics for Dummies. It's actually a great read, but I can't vouch for anything you may be studying. I also have the C++ For Dummies and I enjoy that one just as much.

I also recommend Pre-Calculus Demystified It's got TONS of material and is a very useful resource. Loads of examples and shows steps with wording, etc .

If you're needing help in math related to engineering, it really helps if you understand why the formula is the way it is. Start understanding how a formula works, and how it pertains to the applied part of your studies and the math will make sense and thus will become easier.

As others have mentioned, you can use various online resources such as Khan Academy. I'm assuming you know basic arithmetic (multiplication, exponents, working with fractions, percentages, etc...), if not you'll have to start with that. After that, you may need to learn what is usually called "Pre-Calculus". These are the topics you need to master before you can start learning Calculus. Usually they include study of functions (polynomials, logarithmic, etc...), trigonometry, analytic geometry.

Here's a list of stuff you should investigate:

• Arithmetic Refresher: Improve your working knowledge of arithmetic
  
  
• US Navy mathematics courses
  
  This is a collection of PDFs which are taken from some US Navy mathematics courses. The courses are:
  
  >US Navy course - Mathematics, Basic Math and Algebra NAVEDTRA 14139
  
  >US Navy course - Mathematics, Trigonometry NAVEDTRA 14140
  
  >US Navy course - Mathematics, Pre-Calculus and Introduction to Probability NAVEDTRA 14141
  
  >US Navy course - Mathematics, Introduction to Statistics, Number Systems and Boolean Algebra NAVEDTRA 14142
  
  The Basic Math and Algebra course covers arithmetic and could be used instead of the Arithmetic Refresher, if you'd like.
  
  You may also want to look into books on world problems, as that's where most people have difficulty with. World problems mirror our real-life problem solving process, where we have to translate some real problem into mathematical language in order to tackle it.
  
  
• http://www.artofproblemsolving.com
  
  > The Art of Problem Solving mathematics curriculum is specifically designed for outstanding math students in grades 6-12, and presents a much broader and deeper exploration of challenging mathematics than a typical math curriculum. The Art of Problem Solving texts have been used by tens of thousands of high-performing students, including many winners of major national contests such as MATHCOUNTS and the AMC.
  
  If you look at their bookstore, you will see that they have books for the various subjects your kid will encounter during school. They also have the Beast Academy which is an on-going project to release books for kids in grades 2-5.
  
  Note that they say that the books are for gifted math students since the exercises are taken from math competitions. What's nice about these books though is that they offer the full solutions (not just a final answer, but the full explanation). Also, for every book they have a Diagnostic Test (pre-test) to check and see if you are capable of starting the book.
  
  
• Pre-Calculus stuff...
  
  There are plenty of various Pre-Calculus books which contain all this material. I can't really recommend anything with certainty since I've never read any.
  
  But here's a book you could try by a well-known mathematician who also seems to write really well (it also appears to have solutions to the problems):
  http://www.amazon.com/Precalculus-Prelude-Calculus-Sheldon-Axler/dp/1118083768/
  
  
  ---------------------------
  Once you have some specific subject you're having difficulty with, you can always ask for help or look for a friendly book. The problem with math is that some authors/teachers teach subjects very dryly, so it makes it boring... the challenge for people who aren't naturally motivated for maths is to find teachers/books that excite the student -- and there are a few authors that can do it, so you just have to ask around.
  
  By the way, you should also look for various popular math books that could make studying the subject all the more interesting.

Like others have said, I think you'll do better if you cut out the extra class and reading and focus on doing more problems. Ways to find extra problems;

1. Schaum's Outline of Precalculus - 738 Solved Problems + 30 Videos.
   
   https://www.amazon.com/Schaums-Outline-Precalculus-3rd-Problems/dp/0071795596
   
   2)Precalculus | Khan Academy
   
   https://www.khanacademy.org/math/precalculus
   
   Learn precalculus for free. Full curriculum of exercises and videos.
   
   3)IXL is a paid online service, but it isn't too expensive. No lessons, just lots of problems, and they give you a thorough explanation of what you should have done if you get a wrong answer. It's geared towards kids, so as an adult I had to sign myself up as both a student and a "parent".
   
   https://www.ixl.com/math/precalculus
   
   Also, Youtube videos can be helpful. I'm reviewing algebra/pre-algebra right now. I use both Khan and IXL. Khan has short instructional videos. They are very well-done, but sometimes I like to hear a different take on things. There are a ton of great math teachers on Youtube, and most of the videos are short - like 5-10 minutes. Look up precalc playlists. This would be a quicker, more efficient way to get some of the benefits of attending a 2nd class, like you are doing now, and also could be helpful if you don't think you understand a topic well enough from class and your textbook alone. You can also find the Khan Academy videos on YT, and they also run 5-10 minutes each. Here are some precalc playlists by teachers I like;
   
   https://www.youtube.com/playlist?list=PL0o_zxa4K1BU5sTWZ2YxFhpXwsnMfMke7
   
   https://www.youtube.com/playlist?list=PL3Ip1JQi4mmI9P7QBzU-x2JFNyqSF2Nfz
   
   https://www.youtube.com/playlist?list=PL4FB17E5C77DCCE69
   
   But, also I would encourage you to look at your overall goal. It might make more sense to just stay in political science or switch to a similar major, rather than rack up debt to add on two and a half extra years to your undergrad degree taking difficult math classes that probably won't increase your chances of law school admission.
   

I would highly recommend the "Weird" Series. They are separated into different states, but there are also two volumes for the USA as a whole and one that is all about the weirdness in England. The books cover all aspects of the bizarre in local areas from cryptids and ghosts to unusual buildings and people who lived in these places. I know that I loved these books myself as a kid, and they were largely responsible for my own infatuation with the supernatural. Here's a link to one of the first (and most popular) book in the series: http://www.amazon.com/Weird-U-S-Americas-Legends-Secrets/dp/1402766882 Hope you and your family have a happy holidays :)

I usually use patrickjmt, but you could try scanning Coursera for classes in pre-calculus or trig. Basically it's free online classes that last a few weeks. If not, I use this book as well. It may be from The Complete Idiots Guide series, but it's actually really helpful! A friend who majored in math used this one as well as the calculus book by the same author during his studies. Both are really helpful tools.

ProfRobBob Youtube - This sir has great videos. His playlists are in order and very useful for Calculus. Loved his pre calculus playlist.

Patrick JMT - I could not have passed Calculus 2 without this guy. For the most part, his Calculus section is in order on his website.

KhanAcademy - Nice courses with problems available for you. Really easy to use and navigate. I worked through Algebra and only watched his videos on Trigonometry and Calculus.

Hope you get back on track buddy. Don't give up.


I self taught myself Algebra through Precalculus, here are books I used:

1. Practical Algebra - This helped when doing KhanAcademy Algebra course
   
   
2. Precalculus Demystified - Easy to understand w/o having any knowledge of precalculus.
   
   
3. Precalculus by Larson - The demystified book above helped form a foundation that allowed me to understand this book fairly well
   
   
4. Calculus for Dummies by PatrickJMT - This goes great for soliving problems in PatrickJMT's 1000 problem book.
   

Interviews with mathematicians from MIT (haven't read it, but it is leisurely):
http://www.amazon.com/Recountings-Conversations-Mathematicians-Joel-Segel/dp/1568817134

Some good magazines from AMS:
http://www.amazon.com/Whats-Happening-Mathematical-Sciences-Mathermatical/dp/0821849999

If you want to learn some math in a leisurely way (although it does get pretty deep at times):
http://www.amazon.com/Concepts-Modern-Mathematics-Ian-Stewart/dp/0486284247

A good book on the history of mathematics:
http://www.amazon.com/Mathematics-Nonmathematician-Dover-explaining-science/dp/0486248232

I'll definitely check out that Poincare book, it looks good!

Intro Calculus, in American sense, could as well be renamed "Physics 101" or some such since it's not a very mathematical course. Since Intro Calculus won't teach you how to think you're gonna need a book like How to Solve Word Problems in Calculus by Eugene Don and Benay Don pretty soon.

Aside from that, try these:

Excursions In Calculus by Robert Young.

Calculus:A Liberal Art by William McGowen Priestley.

Calculus for the Ambitious by T. W. KORNER.

Calculus: Concepts and Methods by Ken Binmore and Joan Davies

You can also start with "Calculus proper" = Analysis. The Bible of not-quite-analysis is:

[Calculus by Michael Spivak] (http://www.amazon.com/Calculus-4th-Michael-Spivak/dp/0914098918/ref=sr_1_1?s=books&ie=UTF8&qid=1413311074&sr=1-1&keywords=spivak+calculus).

Also, Analysis is all about inequalities as opposed to Algebra(identities), so you want to be familiar with them:

Introduction to Inequalities by Edwin F. Beckenbach, R. Bellman.

Analytic Inequalities by Nicholas D. Kazarinoff.

As for Linear Algebra, this subject is all over the place. There is about a million books of all levels written every year on this subject, many of which is trash.

My plan would go like this:

1. Learn the geometry of LA and how to prove things in LA:

Linear Algebra Through Geometry by Thomas Banchoff and John Wermer.

Linear Algebra, Third Edition: Algorithms, Applications, and Techniques
by Richard Bronson and Gabriel B. Costa.

2. Getting a bit more sophisticated:

Linear Algebra Done Right by Sheldon Axler.

Linear Algebra: An Introduction to Abstract Mathematics by Robert J. Valenza.

Linear Algebra Done Wrong by Sergei Treil.

3. Turn into the LinAl's 1% :)

Advanced Linear Algebra by Steven Roman.

Good Luck.

Hi,

I'm a TA in my school's CS theory course (a mixture of discrete math, and the automata, languages and complexity topics most CS theory courses cover).

As others have said, "theory" is pretty broad, so there are an awful lot of resources you could look at. As far as textbooks go, we use two - Sipser's Introduction to the Theory of Computation (which others have recommended), and the freely available textbook Mathematics for Computer Science, by Lehman, Leighton and Meyer - which concentrates more on the "discrete math" side of things. Both seem fine to me. Another discrete-math–focused set of notes is by James Aspnes (PDF here) and seems to have some good introductions to these topics.

If you feel that you're "terrible at studying for these types of courses", it might be worth stepping back a bit and trying to find some sort of an intro to university-level math that resonates for you. A few books I've recommended to people who said they were "terrible at uni-level math", but now find it quite interesting, are:

• Keith Devlin, The Language of Mathematics: Making the Invisible Visible
  
• Ian Stewart, Concepts of Modern Mathematics
  
• Martin Liebeck, A Concise Introduction to Pure Mathematics (rather terser than the previous two, but still a lot gentler than some uni-level texts)
  
  These aren't specific to computer science, but might be of help. Good luck!
  
  
  

To answer your second question, KhanAcademy is always good for algebra/trig/basic calc stuff. Another good resource is Paul's online Math Notes, especially if you prefer reading to watching videos.

To answer your second question, here are some classic texts you could try (keep in mind that parts of them may not make all that much sense without knowing any calculus or abstract algebra):

Men of Mathematics by E.T. Bell

The History of Calculus by Carl Boyer

Some other well-received math history books:

An Intro to the History of Math by Howard Eves, Journey Through Genius by William Dunham, Morris Kline's monumental 3-part series (1, 2, 3) (best left until later), and another brilliant book by Dunham.

And the MacTutor History of Math site is a great resource.

Finally, some really great historical thrillers that deal with some really exciting stuff in number theory:

Fermat's Enigma by Simon Sigh

The Music of the Primes by Marcus DuSautoy

Also (I know this is a lot), this is a widely-renowned and cheap book for learning about modern/university-level math: Concepts of Modern Math by Ian Stewart.

I only have one, it's not Algebra or even a site, but it's a good book.

• Rapid Math: tips and tricks
  
  It focuses on arithmatic, but allows you to do some of the same things that 'math geniuses' can do. Very handy, but read the other reviews so you can see what the strengths and weaknesses are. There is a sequel "More Rapid Math: tips and tricks". Starts out slow, so don't blow it off as too easy based on the first chapter or two. The best thing about it is that it will give you a good feel for numbers beyond the tricks that are taught in the book.

Just change your reference number to something that can be used easily, such as 50, 20, 10, 100, 1000, etc. Then you just take the numbers, such as 45 and 55, for ease of use, set 50 as the reference. 45 is 5 below 50, so -5 for its # and +5 for 55. Then add their number to the opposite number, so +5 to 45 or -5 to 55; it always comes out the same. You get 50; multiply the result with your reference number, so that gets you 2500. Then to tie it all off, add the product of your 45 and 55's initial differences from the previous result, +5 (-5) = -25. 2500 + (-25) = 2475.

It's easier to see if you write it out like that guy has it

50) 55 45

50) 55 45
+5 -5

50) 55 45 (The product of [the sum of one of the differences and the
+5 -5 opposite multiplicand] and the reference number)


50) 55 45 2500
+5 -5

50) 55 45 | 2500
+5 -5 |+ (-25)
-------
2475

Like we've said in this thread, it's not magic. It just takes advantage of the distributive property, given you have a good grasp of decimal (i.e. base 10) mathematics.

Speed Mathematics by Bill Handley

Honestly, Trigonometry isn't so rarified a field that you couldn't just go with the Schaum's Outlines series. They're cheap, can be had at pretty much any bookstore, and contain solved exercises.

There may be a textbook with a solutions manual; a cursory search of Amazon shows solutions manuals for a variety of trig books that can be had for pretty cheap. If you have enough discipline, you might be able to simply use the solutions manual without a textbook (most show the problem statement before delving into the solution).

Trig instruction is pretty standardized. I wouldn't worry too much about which book you get; just get any and start doing exercises over and over.

That really depends on you, but my high school taught them as a single one-year course (if you were on the accelerated track), so doing it in a year should be possible with enough motivation on your part. It will of course be easier if you take a lighter courseload. Maybe take a study hall period and use it to work on math. (In my experience, though, study hall was a hard place to get anything done because other students just went there to screw around.)

A lot of people studying at that level use Khan Academy. It's supposed to be pretty good. Other people can probably suggest other online resources.

As for books, Algebra 2 and Precalculus are often taught out of the same book. Books that are titled "precalculus" usually include a section on limits that you might not need to cover (ask about this) because it's part of Calculus I.

You can get free textbooks here:

• https://openstax.org/details/algebra-and-trigonometry
  
• http://www.stitz-zeager.com/
  
  These are some suggested dead tree books:
  
  
• Axler, Precalculus (sorry, this used to be cheaper but it looks like the fall semester started and the students bought up all the cheap copies)
  
• Foerster, Algebra and Trigonometry
  
  Or just see if your school will let you borrow a copy of the textbook that they use.
  
  Whatever you choose to use, I suggest that you use multiple resources to get some different points of view and a wider variety of problems to work on. This is especially important since you won't be going to class.
  

These aren't novels, but I really enjoyed these books around that age:

The I Hate Mathematics Book

Math for Smarty Pants

They taught me a lot of fun math puzzles and concepts for the first time (prime numbers, perfect numbers, basic combinatorics, math magic tricks), each with a bit of a story attached.

Here's an easy read that I liked: Concepts of Modern Mathematics by Ian Stewart. It gives a pretty broad overview. And you can't beat the price of those Dover paperbacks.

You may also be interested in a more thorough exploration of the history of the subject. Try History of Mathematics by Carl Boyer.

Guys, thank you for your tips. I am looking it those. I didn't reply sooner because of family issues (grandpa had 2 strokes and had surgery), but all seems well now.

I was able to get, for free, a copy of this book from my cousin: http://www.amazon.com/Precalculus-9th-Edition-Ron-Larson/dp/1133949010 (Precalculus, 9th Edition by Larson).

Going to start going through it now. It has a good bit of trig and I think while it may not cover more basic algebra topics, it lets me know what I need to review on my own. The appendix also does a brief explanation of simpler topics.

W method;' write everything.

Get a book with solutions in it, and then WRITE the examples as you follow them along with the solutions.

Yes, it is a huge amount of work, but it will save your life.

A good starting book is any Schaum.

Columbus: 2,078,723 > Cleveland: 2,058,844

>had a difference in 3,000

The difference is 19,879, and while Cleveland has shrunk since 2010, Columbus has surged by over 9%.

I know that you want to be right, but unfortunately you are not. [I recommend this book to help you in the future!] (https://www.amazon.com/Basic-Math-Pre-Algebra-Dummies-Science/dp/1119293634/ref=sr_1_1?ie=UTF8&qid=1537499491&sr=8-1&keywords=basic+arithmetic). Best of luck!

What is up with that Calculus course? From Limits to Lagrange Multipliers & ODE's in a single semester? If your course is covering all that material then he is done for. That is pretty much Calc1-3 without vectors in a single semester.

I'd suggest spending the entire month finishing a good pre-calc book (ebook is easy to find). And praying.

Many thanks for the suggestions!

For the interested, I bought this book for GT:

http://www.amazon.com/Introductory-Graph-Theory-Gary-Chartrand/dp/0486247759

I also was tempted by the following book:

http://www.amazon.com/Concepts-Modern-Mathematics-Ian-Stewart/dp/0486284247



I think buying a book feels better than sex. (I can compare.)

These are different fields (programming vs math etc) however I will ask you, do you like math or programming ? If not maybe you need to get to know these quite interesting fields better. For math I would recommend one of the Dover introduction books, such as Ian Stewarts' concepts of modern math.

How about selected chapters from Stewart's Concepts of Modern Mathematics? It has a pretty wide range of jumping off points and is a relatively affordable Dover book. You could go into more or lesser detail on these topics based on the students' backgrounds.

Another idea would be to focus on foundations like set theory, logic, construction/progression of number systems from ℕ -> ℤ -> ℚ -> ℝ -> ℂ , and then maybe move into some philosophy of math. There could be some fun and accessible class discussion, such as having them argue for or against Platonism. [Edit: You could throw in some Smullyan puzzle book stuff for the logic portion of this for further entertainment value.]

I teach middle school and use many of the mental math shortcuts in this book, Arithmetricks.

If that book doesn't keep you busy enough, then move on to Rapid Math and its sequel.

If you like videos, these are effective and fun:
Mental Math Secrets - Volume 1 - done by Jason Gibson of the MathTutorDVD series. Short, sweet, and to-the-point.

Since people have already mentioned Arthur Benjamin's book, I'm going to suggest his more enjoyable video from The Great Courses, The Secrets of Mental Math. (It's expensive, but goes on sale, so watch for them.)

https://www.amazon.com/College-Algebra-12th-Margaret-Lial/dp/0134217454/ref=sr_1_4?ie=UTF8&qid=1550277393&sr=8-4&keywords=college+algebra+textbook


I've never read this book, but by looking at the table of contents, it seems pretty good.

The I HATE MATHEMATICS! Book

Math for Smarty Pants

I remember picking up both of these books at -some- point during elementary school book fairs. I have always really liked math, but they do have some interesting topics and random facts. The topics are always pretty short - I remember quite a few on statistics in various forms. I'm not sure they would 100% work for what you are looking for but they might be able to form springboards for projects?

Got Ds and Fs in math throughout middle/high school.

Took my first math class at the ripe age of 30 in college; could barely do simple multiplication/division so I started from the ground up by taking the most remedial course.

3 math classes later (all A+) I'm now in pre-calculus, tutoring other students, and planning to teach math at a high school or college level. Khan Academy and Pre-Algebra for Dummies by Mark Zegarelli were huge helps for getting me up to speed (which is good, because 2 out of 3 of my teachers weren't very good at teaching).

I grew up with the idea that I was "bad at math" and I internalized this idea as a "truth". I had internalized the idea to such an extent that it influenced my entire educational and professional career; I actively avoided any STEM degrees and went into law instead. I threw away my potential because of the lie/self-degradation that some people are simply "bad" at math. I wasn't bad at math; I just didn't have the tools I needed to succeed.

Today I have my choice of teachers, teacher review sites, video tutorials like Khan Academy, alternative text books, and text book reviews. I didn't have those tools as a high school student. High school math was an exercise in humiliation and debasement. I want to be a math teacher because I NEVER want another student to feel the way that I felt.



EDIT 1: Thanks for the gold stranger!

EDIT 2: Here's the book I used to prepare me for my first math class. It's a newer edition than the one I used:

https://www.amazon.com/Basic-Math-Pre-Algebra-Dummies-Zegarelli/dp/1119293634/ref=sr_1_4?ie=UTF8&qid=1481730619&sr=8-4&keywords=pre-algebra+for+dummies

To anyone interested, this method is used in this book, as well as other mathematical shortcuts.

Enjoy.

http://www.amazon.com/gp/aw/d/0471467316

It really depends which direction in mathematics you want to go. Even as a math major, I didn't really understand how vast it was until I got into abstract math.

My favorite way to learn is browse Amazon for "Dover Books on Mathematics." They are generally had for a penny + shipping if you don't mind buying used.

A good intro into modern mathematics: https://www.amazon.com/Concepts-Modern-Mathematics-Dover-Books/dp/0486284247

Thank you very much. I was considering also getting this book (http://www.amazon.com/Pre-Calculus-Demystified-Rhonda-Huettenmueller/dp/0071439277) to kind of guide me in studying. Now that it is presented to me, Khan Academy looks like it could be a good supplement.

If you want a fairly solid explanation on what arithmetic really is I recommend Frege's "The Foundations of Arithmetic". It's not the final story (Peano simplified the formal details afterwards) but I found it enlightening nevertheless.

[Precalculus with Limits 1e] (https://www.amazon.com/Precalculus-Limits-Ron-Larson/dp/0618660895/ref=sr_1_4?ie=UTF8&qid=1527656177&sr=8-4&keywords=larson+precalculus+with+limits) is a great book.

Beyond comprehensive coverage of the various types of functions (including logarithms and exponentials), trigonometry, and an introduction to complex numbers, the book covers [limits] (http://prntscr.com/jodi0c) and has a brief intro to [vectors] (http://prntscr.com/jodi3z), 3D space, the dot product, and cross product.

I enjoyed Concepts of Modern Mathematics when I was in high school. It might be a little basic and it's a bit uneven in places. But it's a really good lay account of the basic notions in "modern" mathematics. It doesn't really mention so much the various fields. For that, surfing Wikipedia is hard to beat.

Firstly, I would highly recommend camping over staying in motels/hotels, so take a route that allows this. I took a long road trip a few summers ago and picked destinations based on awesome places to camp, and had a killer time. That being said, Yosemite was fucking gorgeous, so maybe head that way?

Also check out the book Weird U.S. for some strange stops.

try renting them from amazon or barnes and noble. do NOT ever buy from the bookstore. their markup is crazy.

here's amazon: http://www.amazon.com/Precalculus-Ron-Larson/dp/1133949010/ref=sr_1_1?ie=UTF8&qid=1406429589&sr=8-1&keywords=precalculus+textbook+larsen#selectedObb=rbb_rbb_trigger

here's b&n (cheaper) http://www.barnesandnoble.com/w/precalculus-ron-larson/1100200816?ean=9781133949015

they're both 9th edition though. I'm sure if you actually only need the 6th, that will be even cheaper.

also: most teachers/departments will put a copy put on reserve all semester.

I think there could do some really cool analysis tracing lines of thought and how they developed or comparing what was in vogue in math to world developments at the time. This book might be a good overview for modern developments and this one has a overview of the development of math through history

Concepts of Modern Mathematics by Ian Stewart is an excellent book about modern math. As is Foundations and Fundamental Concepts of Mathematics by Howard Eves I would recommend these two along with the far more expensive Naive Set Theory by Halmos

Mathematician here, with a couple of observations:
First, yep, you're expected to teach yourself. Homework is the principal means of learning math.

Second, as far as what "a, b, c" are, try another book. Lots of my students have liked Precalculus Demystified.

I took a trigonometry class at a CC. It was two weeks of material stretched out to a full semester.

In six weeks you should be able to learn all the trigonometry you'll ever need, with plenty of time left over.

If you want to raise the bar a little higher, I suggest you get a hold of [Axler's Precalculus] (http://www.amazon.com/gp/offer-listing/0470416742/ref=dp_olp_used?ie=UTF8&condition=used). It's a very well-written book that teaches all the information you'll need to be successful in calculus, including trigonometry.

If you're bright at math it should be possible to master both these topics in six weeks, assuming that you can put adequate time in daily. These subjects, as they are taught in high school or early college courses, are very mechanical. You just need to drill, drill, drill the hell out of them until they are second nature.

The I Hate Mathematics by Marilyn Burns is a classic and fantastic for extending mathematical thinking. She has a whole line of fun books.

This one is pretty good

You know, I've had it for so long that I don't even remember where I got it from. Here is the book on Amazon, and here are a ton of cheap, used ones from Barnes and Noble, if you don't care about it being used.

I don't know exactly what math class you're in, but the "Schaum's Outline" series contains a ton of solved problems. They're also MUCH cheaper than buying a textbook.

Like I said I'm not sure what your skill level is, but here are a few I found on Amazon.

Precalculus

Trigonometry

Calculus

prof Leonard only does from calc afaik.

If you want a book suggestion for Precalc I would recommend this

https://www.amazon.com/Precalculus-Prelude-Calculus-Sheldon-Axler/dp/0470416742

Mathematics for the Nonmathematician, disgustingly eurocentric but still good, Concepts of Modern Mathematics gives an overview of some higher maths, and I have the set The World of Mathematics which I occasionally read a random chapter, it covers lots of ground.

I've come accross these tricks before in Rapid Math Tricks & Tips. Useful stuff back in middle and high school on math team.

Before the Princeton Companion to Mathematics, there were:

What Is Mathematics? by Courant and Robbins

Mathematics: Its Content, Methods and Meaning by Aleksandrov, Kolmogorov, and Lavrent'ev

Concepts of Modern Mathematics by Ian Stewart

https://www.amazon.com/College-Algebra-12th-Margaret-Lial/dp/0134217454/ref=sr_1_1?ie=UTF8&qid=1484951902&sr=8-1&keywords=college+algebra+12

There's a couple pages about him in the book Weird US. If I remember correctly, he traveled the route with such accuracy that he always showed up in the same places within several hours of when he was expected to arrive.

Fred Safiers Schaum's Outline of Precalculus, 3rd Edition {Schaum's Outline Series}.

I suggest you get this book: http://www.amazon.com/Rapid-Math-Tricks-Tips-Number/dp/0471575631

It has a lot of them.

Check out:

• Concepts of Modern Mathematics by Stewart
  
• Mathematics: Its Content, Methods and Meaning by Aleksandrov, Kolmogorov & Lavrent’ev
  
  

Start with this

https://www.amazon.com/Basic-Math-Pre-Algebra-Dummies-Lifestyle/dp/1119293634/ref=sr_1_1?ie=UTF8&qid=1505151378&sr=8-1&keywords=mathematics+for+dummies

Rapid Math Tricks & Tips: 30 Days to Number Power

by Edward H. Julius