Rebuilding Math Foundations: Reflection on a Late Start

[vikingofsixth]

The short summary is that my high school foundations of math were absolutely terrible as I was instructed from the youngest age that mathematics was entirely about computation and that being talented in math meant being able to handle lots of number grinding in your head without a calculator. I am a very visual and mechanical person so I failed terribly at this and was quickly ruled out of higher mathematics before I even entered college.

Now I am very close to finishing a degree with philosophy and language and the greatest regret I have is my knowledge of mathematics. Very early in my college career after taking propositional logic and first order logic I realized how much I loved playing with these formal languages. An enjoyment that seems much more pure than constructing anything with a natural language. Not to long ago I was speaking to someone about my math history and he laughed replying 'math is not about computation'.

Every time I walk into a classroom and see a chalkboard covered from side to side with some sort of problem from the higher level math classes I realize they are not dealing with numbers but with ideas. And I am damned upset that I do not know how to use their language!

I have a lot of free time this fall and want to rebuild my math foundation from the ground up. I am certain I have a good deal of the logical and language background to help me along the way but I am not sure how to start. Having never stepped foot in a Calculus class I need to revisit everything from trig to algebra! Does anyone have any advice or should I just let this peaked interest go because it is too late?

 

[phinds]

I'll leave it to more math knowledgeable folks to give you specific direction, but I ASSURE you it is NEVER too late if you genuinely want to learn it, as you seem to.

 

[jbunniii]

Having never stepped foot in a Calculus class I need to revisit everything from trig to algebra! Does anyone have any advice or should I just let this peaked interest go because it is too late?

Of course it's not too late. If you are motivated and have the time, then all you need is a good textbook and a place to ask questions, such as this forum. This book should cover what you need: Basic Mathematics Don't just read it - also do as many exercises/problems as you can. That is the only way to really learn mathematics.

 

[Rasalhague]

Hi, Viking of Sixth! I was in a very similar position to you. In 2008, I get into the regular habit of watching online video lectures on a wide range of topics, including some of the chemistry lectures at MIT Open Courseware. I also read a little introductory book on logic. In this way, I overcame my automatic fear of symbolic formulas, and caught a glimpse of the treasure trove of learning materials that are becoming available online. By the end of the year, I'd resolved to learn some mathematics.

I started on the Khan Academy videos, right at the very beginning. Just like you, my high school foundations were pretty shaky. So I took as much time as I needed to get clear on the basics. I considered no question too humiliatingly basic to ask! I obsessively practiced simple arithmetic and algebra, then trigonometry. Then I borrowed a calculus textbook which I worked through as I continued to watch the Khan Academy videos. I started on the MIT single variable calculus videos. I eventually also watched a lot of their lectures on multivariable calculus and linear algebra and physics.

I have a brother who got part-way through an undergrad course in mathematics and a sister who's a physicist, so I was lucky to have people I could ask questions of, and borrow textbooks from. I took ruthless advantage of that! I'm interested in mathematics in general, including pure math, but decided to concentrate on topics with applications in science, just as a way to prioritize and choose among the profusion of possibilities. So: calculus, linear algebra, a little statistics, and I really ought to get a bit further into differential equations...

At some point, I was reading Benjamin Crowell's online textbook Simple Nature and was thrilled to find I could actually follow his explanation of how space and time relate to each other in special relativity. This was a turning point as it set me on the long road to learning enough differential geometry (a branch of mathematics that draws on topology, calculus, and linear algebra) to understand at least the principles of general relativity - an ongoing project. I've been dipping into Michael Spivak's wonderful (and wonderfully cover-illustrated) books on the subject (diff. geom.) in what little spare time I can muster these days. I just completed Coursera's free online course in Quantum Mechanics and Quantum Computing, main requirement basic linear algebra.

I was drawn to mathematics for several reasons. For one, it's personally interesting as a way of balancing my education, becoming more at home in a universe where mathematics plays such a role at so many levels, deep and practical, and of expanding my understanding into more general, universal areas. I relish the challenge of it, the chance to test myself objectively - especially coming from an arts background where success is often measured more subjectively. Mathematics has been called the science of patterns, and there's a deep esthetic element to my attraction: think of fractals, music, patterns sensory and abstract. (Have you read Keith Devlin's book The Math Gene? He very much emphasizes how mathematics is all about ideas rather than mere skill at calculating.) There's another delight: the way that mathematics extends the senses, and allows us to contemplate patterns in nature that we'd otherwise not be aware of, and indeed to conceptualize things that otherwise we'd not be able to even think about. I like the idea that, in learning mathematics, I'm exploring this landscape which is nonphysical yet, in some curious way, objective. Roger Penrose has some fascinating things to say about the the philosophy of this in The Road to Reality. Oh, and it's always exciting to find hidden connections between things. It can be like looking behind the scenes of nature and noticing how apparently diverse phenomena manifest some common principle. It's also great for distraction/entertainment/escapism/meditation; and coming to it late, after having nearly given up on the idea of ever indulging this interest, I really appreciate each little bit of progress I make. Oh, oh, and it gives you a whole store of metaphors and new ways of conceptualizing non-mathematical things, new ways of thinking in general, that may be useful in unpredictable ways.

In short, my advice is: go for it! I've gone the route of self-study so far, but maybe others here can comment on other possibilities, such as face-to-face courses.

 

[member 392791]

I don't think Fermat studied math until he was in his 30's..and he wasn't even a full time mathematician and ended up making major contributions to the field.

 

[dustbin]

I don't think Fermat studied math until he was in his 30's..and he wasn't even a full time mathematician and ended up making major contributions to the field.

Quoted from wikipedia
"He attended the University of Toulouse before moving to Bordeaux in the second half of the 1620s. In Bordeaux he began his first serious mathematical researches and in 1629 he gave a copy of his restoration of Apollonius's De Locis Planis to one of the mathematicians there. "

He was, according to the same page, born in 1601.

 

[member 392791]

ok 28 years old, my bad. He studied law at university.

 

[dustbin]

Not trying to be a jerk, I was just posting it out of interest. I was interested by your claim (especially since I am writing a series of papers about the history of calculus for a class) and thought I would supply the specifics in case anyone else was interested.

 

[CallMeShady]

Well, being specific and to the point, I would suggest that you check out Khan Academy. The "lecture" videos provided by Khan have been amazing and I continue to watch his videos when I don't understand a concept at school. You have the option to choose topics that range from algebra to trig, and you can quiz yourself at the end as well.

I am not affiliated, and nor am I promoting that site. I think that Khan Academy will be resourceful in your case since you don't have to pay for tuition, and you can start learning at your own pace.

 

[FreeMitya]

I'm in a similar situation as you (however, judging by where you said you are in university, probably quite a bit younger, so I don't think I feel as much pressure). I want to study physics, and my primary burden has been my neglect of mathematics. Most of my maths teachers have been mediocre at best; they understood the concepts, but they didn't seem to love mathematics and apparently didn't appreciate the stunning beauty of them ( they had a very utilitarian approach, so to speak), so nobody really inspired me until I came to this revelation on my own (but here I go again blaming others for my drawbacks).

Anyway, you're not alone, and I wish you all the best in your journey through the riveting labyrinth that is mathematics. The best advice I can give you at this point is to never be afraid of not understanding something and never be afraid of asking questions.