I am a second year college student who always slacked off in most classes in school and uni, especially math. However, I have just recently gained a new appreciation for math, science, and general logic. I realize I was stupid for slacking off in math all these years since it is used for almost everything. I would like to start mathematics from the very beginning (arithmetic, number theory, etc) and work my way up to the level I should be at now or higher. One of the main reasons I slacked off in math in HS was because I felt the teachers were teaching it wrong (of course no one else shared this view since they just wanted the grades, not to actually know the content). I feel like I've figured out how I learn best and would like to apply these techniques to my study of math.
One of the strategies I use, if not the most important, is getting a big-picture feel of the subject matter/discipline. I've always had this idea in the back of my mind but never believed that this could have practical applications, until I watched the Domain of Science's 'Map of Mathematics' video on Youtube (they also have a map of physics and map of chem) where he attempts to map out all of math in a way that connects it all together. I love the idea but it still isn't substantial enough for me. I believe any discipline, especially one as well established as math, can be organized in a way that shows how the study progressed from its origins to now and how these connections/links formed that made it such an interconnected subject matter. That way anytime I am studying any area of math, I will better understand how that specific area relates to the entirety of math, where it originated from, how it could apply to completely different areas of math, etc. The way teachers/professors teach math (at least in my experience) is that they try to shove as much content into you per semester, sometimes even cherry-picking what they can teach the most of or what students seem to grasp most, leaving out other important aspects of math. Or they teach the content with absolutely no relation to its applications to real-world problems. I am 20 and I still have not once been taught how linear algebra, for example, applies to the engineering or pharmaceutical industry, if it even does? Another problem I have with institutionalized math is that they make it seem like you can only be really good at it if you just naturally have a knack for it. I believe that is completely wrong because maths is a learned system, not a skill like soccer (where in the end of the day, no matter how much or hard you train, you either have that natural ability or you dont). I've been reading a book called A Mind For Numbers (Barbara Oakley) in which she discusses ways of improving one's math level, no matter what stage they are at. She herself hated math throughout he whole childhood and didnt take it seriously until she was 26 in a Trig class. She eventually got a PhD in Math. And she also gives real-life examples of other people who realized their passion for math later on in life and succeeded in fulfilling that passion. So I absolutely do not believe that being gifted in math really makes any difference on the fundamental level (of course maybe when you get to much more advanced applications of math, but I'm not even interested in that).
However, because of my major and my career intentions after graduating it doesn't seem like I'll be leaving the realm of institutionalized math anytime soon. Which is fine, so long as I make up for this waste of time by conducting my own strategies for learning and mastering math. My goals are as follows:
-I want to redo math from the very beginning. I want to absolutely master the very basic fields like Arithmetic and so to the tee. And I am not just talking about the levels of Arithmetic and Geometry they teach in school, but the entirety of it or at least have an understanding of what the entirety of it looks like.
-I want to map out all of mathematics in a systematized and to-the-point way so as to have a 'big picture' feel to it which I can use as a reference point for when I am studying any area of math; to see how it originated and how it relates to the rest of mathematics.
-I want to reach the level where I can fully comprehend the fundamentals of Math up to (and maybe including) Calculus, for now at least. I want to be comfortable in applying any math up to this point to any subject like Chemistry, Biology, Physics, Economics, Statistics, Computer Science, etc. Through personal anecdotes I KNOW for a fact that this will help me not just better strengthen my fundamental math skills but also understand and master the subjects I'm using them for.
-I want to read books about Math or how Math relates to other things. So far I have read 'A Mind for Numbers' and 'Errors, Blunders, and Lies: How to tell the difference'.
-I want to know about the people who made math what it is and how they came up with their conclusions/discoveries, etc.
Of course, my main question to you is how you believe I should tackle these goals? What is your advice? I have other smaller questions to ask too tho:
-What textbook(s) should I use? I've always loathed monotonous textbooks because they are too technical and dont offer any real-world examples or applications. With those kinds of textbooks, I learn what I need for that semester or even that week very well, but not in the way that it sticks in mind on some fundamental level. I prefer textbooks that are more engaging in a real-life sense. I recently discovered the Springer Undergraduate Math Series which is a math textbook series that is quite different from the norm; they have small textbooks for each specific subfields of the major fields of math. The textbooks are small but very concise and are quite interesting to read/study from not just because of its unique take on Math teaching but also because of its real-world examples/applications. Are there other textbooks like this? I know that of course there is no general consensus as to what the best math textbooks are, but are there any that seem to be of the best learning value?
-What nonfiction books about or relating to math would you recommend? Doesnt necessarily have to be as a study tool, but also for fun.
-Is there a general consensus as to what test is the best at determining math proficiency for all levels? I'd like to be able to monitor my progress as I go. Also, are there other ways to monitor my progress? Khanacademy website seemed useful to me for a while, but I felt it was making things too easy.
-Do you know of any people who started appreciating and/or learning math at a later time in their life? If so can you tell me how I can contact them or if they are historical/famous figures, how I can find out about their story?
-Do you have any general advice regarding my situation and my intentions?
I know that this all has been said before and that everyone believes that they can do this without actually grasping how difficult all this is and the amount of effort that must be put in, etc. But at this point of my life I am determined to do this no matter what. I am fully aware that this endeavor will take a long, long time and that I might not even ever reach the level I want to reach, but I'd rather try then keep on struggling with something that is so deeply rooted in almost everything we do for the rest of my life.