Resources for mathematics

In your IB course you've probably encountered a maths book, which is for most, the book you use in class, whether online or hardcopy. Thus, you might wonder why you should buy any new books when you already have all you need in that book. And, you'd be right. However, there are a couple of reasons for buying other mathematics books in your study of mathematics. Firstly, since the books covers most topics in IB and can't be too long, most of the topics have been more so glanced over and not been studied too deeply. If you have a book that is almost entirely devoted to one topic, you can get a lot more information from it. You really don't have to read the whole, book but just the section you are interested in. This gives you a different perspective of the topic which leads into my second point, that getting a different and in-depth view of a topic will usually lead to better understanding and therefore make mathematics "easier". What I mean by this is that, by reading different books on the same topic, you will gain more knowledge about the topic as the authors of the books have different ways of teaching and therefore has a different understanding or viewpoint of the topic. Thus, if one way of explaining is confusing, the other way might be super clear.

Now onto the books:

Calculus - James Stewart

This book is written and made for university students that take calculus as a course. Thus, the book contains everything you need to know about calculus for most courses anyone is going to take, which includes the IB course. While the calculus you learn in IB is more of a glance than what you find in the book, it is very useful as it is very well made (has nine editions, multiple versions and is very popular) and goes through topics in understandable ways. You can also find many other topics that are important in calculus, but not central in it. For example, there are multiple sections on series and sequences, and if you have physics, you might want to check out the vector section. Overall, the book is just great to have and if you take harder maths in university, then the book will come in handy for you.

There are multiple versions of the book, for example calculus and calculus early transcendences, but the difference is very small, as it is more the order of which things are placed in the book of what is up to the course teacher to decide, but we don't have it like that hence it doesn't matter too much.

All The Math You Missed (second edition) (sort of difficult)- Thomas A. Garrity

All The Math you missed is also a book aimed at university students and more so graduate students, meaning the topics will be well harder than what we have learnt. Indeed, to be able to understand most things in the book, you will have to have had previous university education, which makes sense for graduate students. So the question might be: why is it useful for us? Well, whilst most of the topics are very difficult, they are introduced and taught so that anyone who is quite interested in maths and puts their mind to it, can learn some of the topics in the book. The book does also cover a mental amount of topics meaning that you can get a good overview of some of the requirements you will need to know if you decide to peruse maths. For anyone not perusing maths, it is still a very interesting book that I would recommend you check out (I suppose that's why it's here).

The Art of Problem Solving, Volume 1: The Basics and The Art of Problem Solving, Volume 2: And Beyond

These are books that are actually aimed at upper-secondary school (high school) students. The books are not exactly textbooks and do not directly teach you the different topics, but rather focuses on how to approach problems. Both books has an incredible amount of topics, where the first book gives more of an introduction to the topics and the second book (or second volume) goes more in-depth. The second book is not required, but would be a nice addition to your book collection.

For IB students, the exams are really what matters to most, especially towards your grade in a subject and your overall score. While you have internal assesments, the extended essay and theory of knowledge, which all counts towards your final score, the exams are absolutely paramount in determing your final score and grade in a subject. Thus, revising for your exams is utmost important both throughout the course and as the exams are approaching. The listed websites below are good ways for IB students to practice and revise for their exams.

IB specific websites

The first website we will recommend, is Revision Village: https://www.revisionvillage.com/

Revision Village was primarily made for IB maths, but has now added other subjects like chemistry, physcis, biology and more, all made for IB of course. There's a lot of exercises to do with a mark scheme for all exercises, and a video explaining it for most. The only caviat is that, as with most things, you have to pay to get full access to all the exercises in a subject. You also get access to an AI that can guide you bit. Notice a subject, because you only buy membership for one subject at a time, and it is quite expensive. Althought, if you buy the full course pack, it is basically a one time purchase. 

Another website that is good for maths, and other subjects, is a website called Revision Dojo: https://www.revisiondojo.com/

Revision Dojo, similar to Revision Village, was made with IB students in mind. They offer revison in more subjects than Revision Village and have quite a lot of exercises as well. They have mark schemes for every quesiton and an AI that can help you. If you have a free memeber ship, you have 10 usages every week, but if you buy the membership, which is way cheaper than Revision Village, you have an ulimited amount of uses, along with other benefits. The website also offers tutoring (quite expensive) and flashcards. 

Non-IB specific websites

Khan Academy: https://www.khanacademy.org/

If you don't already know by now, Khan Academy is a good website for learning a lot of things related to most subjects you meet in school. The website is video based with some practice questions and articles sprinkled in between videos. It is also completely free. If there's a topic you're unsure of, checking Khan Academy is always a good place to start as they offer so many videos on so many different things. 

More website recommendations to come...

Often, when most people struggle with maths own their own, they go to YouTube  for advice. This can be seen as an alternative to an actual lecture or class and can therefore be very useful if you are stuck on a particular problem or just don't understand the topic. In addition, they're are many channels that gives some general advice and comes up with some tricks to better solve problems. Other channels, however, might just have general content about maths, not necessarily anything that will directly help you and add to your arsenal of knowledge, but rather boost your inspiration in maths. The last point is sort of important as well. If you don't have any motivation for doing maths in the first place, it can prove quite difficult to get better without forcing yourself to do maths due to an upcoming test or assignment. So, having some reason to do maths can indirectly help you as well.

The following are different channels that might cover some of the aforementioned things.

3Blue1Brown

3Blue1Brown is a mainly a maths YouTube channel, but it does also cover similar subjects, like physics. The aim of his videos is, as he states, to make difficult topics easier by visualizing the ideas. Subsequently, the videos are well made and usually gives you an understanding of the topic. The maths can get difficult, but since he tries to teach by using visual tools, it is usually quite comprehensible. 

tecmath

tecmath is a maths YouTube channel that mainly gives tricks to make problems easier overall. The maths content does not really go beyond the basics of math, but you can find some more advanced videos. The tricks he teaches works really well and with some practice they become powerful tools in your maths journey, especially under an exam where there is a lot of pressure and a simple trick might be all you need to solve a problem. Unfortunately, as of 11.01.24, the YouTube channel has been hacked and is therefore unavailable right now. Hopefully he will able to retrieve his channel, and when that time comes, this page will be updated with a link to his channel. The channel has now been retrieved, and he is back to uploading. I will keep this as a record of when it happened

The Organic Chemistry Tutor

The Organic Chemistry Tutor, despite his name, makes a lot of educational content about all of maths, physics and chemistry. He makes tutorial type videos that are aimed at teaching you how to solve problems and a bit of theory behind solving them. Through this channel you can really learn a lot of useful things that you will, most likely, go through in class. Thusly, this YouTube channel is very good if you are having a hard time understanding something or if you need some revision. Disclaimer: not all of his full videos are free, but there is still a lot of free content for you to consume.

Numberphile

Numberphile is a YouTube channel all about numbers and mathematics. You will not learn anything in extreme detail from this channel, all the videos are made in such a way that the topic of the video in fully understandable, even though the concept and maths behind it is difficult. Personally, I would say the videos they make are more for entertainment and to spread the message of how fun maths are to everyone in the world, so I wouldn't bet on learning too much. However, that's not to say you won't learn anything since the videos are so well planned out.

The Math Sorcerer

The Math Sorcerer is a maths channel mainly focused on ... well, maths. The channel has a variety of content all about maths, spanning from 'how to solve' videos, to maths and general advice, to book recommendations and much more. The maths he solves ranges from basic fractions, all the way to advanced calculus and (for example) matrices. If you need any comfort in the vast world of maths, The Math Sorcerer is definitely the place to go. 

MIT OpenCourseWare

MIT OpenCourseWare is a channel compiled of officially published lectures from MIT, a university in the US. The content you will find on this channel are lectures of different subjects like physics, maths, computer science and more. The maths done here should be mostly be beyond what we learn in the IB, since all of it is made for university students, and often those of high calibre. That doesn't mean it is futile to watch videos on the channel, but it does make it a slightly difficult to follow along the courses they post. I would however, recommend to check them out as they are great fun if you like watching these types of videos. Also, just watching a video or two of the start of a course can be quite insightful.

Tom Rocks Maths

Tom Rocks Maths is maths channel that mainly covers exam question. He does this in a way where he tries to solve exams himself whilst you watch him do it. To make it insightful, he processes all his thoughts out loud so that we can hear how a master of maths solves question that often lie around high school maths. Whilst you might not learn too much from the channel, it can be good to watch his videos since you will understand a bit more of how to think when doing maths and different approaches to exam questions, which is especially important in IB. I would also recommend to just watch his videos, as they are quite entertaining.

Tibees

Tibiees, similarly to Tom Rocks Maths, covers a lot of maths and physics exams. She however, doesn't usually solve all the question, but rather looks at them and might go through how you could solve them. She also makes a lot of videos about famous mathematicians/physicists and their journey in the field. Her videos are probably for those who like watching videos about maths and physics, and you won't learn all that much just watching her videos. Although that is good, as you don't have to spend all your brain power at all times. Still, she has videos that will teach you some concepts which is another reason to watch her.

blackpenredpen

blackpenredpen is a math YouTube channel that goes through how to solve questions. He posts videos where he has one maths problem that he goes through whilst telling the audience what he is thinking, reminding them of concepts and finally how they are solved. The majority of the problems are calculus problems, but you will find many other types of problems. If you are stuck on a trickly problem, it is always a good idea to go to his channel to see if he has done anything similar. You can also just watch him as entertainment, as I do.