Bear with me here on some background: I am taking a Calculus course - the first math course I've taken in over 10 years. (I reviewed basic maths - algebra through basic trigonometry, independently and took a math placement exam and placed into Calculus quite easily.)

In high school (and college, for that matter), I was a blowoff. I daresay I am smart, but I barely paid attention in class. I spent most of lecture time reading science fiction novels and passing notes, but scraped by with A's and B's in my classes (including math) without really thinking about it - I just looked at sample problems and did the work, and went in for extra help if something confused me. I rarely read the book aside from sample problems. I knew I was going to major in art, so I took the minimum amount of math required to get into my university's art program (through Algebra II, which included basic trig), and never gave math much thought.

So here's my observation, now taking a math class for the first time as an adult who is paying attention and not being a blowoff. I am trying to take the course seriously, because hey, I'm an adult and it's my valuable time and money, and at this time, I am exploring the idea of getting a second degree in a science.

So trying to take this seriously - I realize even though I am able to learn to solve problems with relative ease, the nitty gritty of the class I find HIGHLY confusing. I'm taking the course distance learning, so the lectures are over the internet (a tool I never had when I was a college student the first time), and I find I have to replay them over and over again, or read the book excruciatingly slow, in order to get some of the concepts they are describing at the level with which they describe them. (Compared to simply solving a problem, I "get it" the first time fairly easily. I just may not 100% understand WHAT it is I'm doing, if that makes sense.)

I can see how easy it is for students to take the approach I did in high school. If I ignored the book and lectures nearly entirely, I could still solve all the problems and get an 'A' in the course with relative ease.

Now, as someone who is trying to take this seriously, I'm not planning on doing that. I want to crunch the concept into my head and try to understand the material on a deeper and more meaningful level.

My question is, how problematic is it that I am finding it very difficult to do so? Do many serious math and science students have to do the same, or am I deficient? Really, do most serious students who sit in a math lecture and hear mathematical definitions or watch their instructor do proofs of theorems sitting there going "oh, ok" the same way I would if I were listening to a history lecture? Or do others have to go back and really think this stuff through, too? Am I fooling myself into thinking it that I am capable of pursuing a future in the sciences or is my experience something that is to be expected?

I AM able to get it. It's just that the first time I hear something like that in a lecture, my initial reaction is... "WHAT?! I have NO idea what he just said." And I have to spend 10-20 minutes deconstructing one definition to really understand it. This is VERY different for me compared to my experiences with other college courses, where I sit in a lecture, the professor talks, and I just take in the information kind of passively and there's not really anything else to do but reinforce the information so I don't forget it.

The contrast in experiences is making me feel a little dumb. Is this just the nature of the beast? As I get more familiar with "math language" will these lectures become easier to comprehend? Or am I just deficient?

Hello,

I'll tell you some things. It'll be up to you to see whethere this is useful or not...

In high school, I was quite good at maths. Like you, I knew how to do the problems, and got not so bad marks (well, these were not A's, but it's a different system here). But I didn't pay much attention. Just contenting myself with the problems I was given. (and even so, I don't think I did them all ).
Then, I spent three years without doing any math. Doing physics, biology, etc...
After that, I was accepted in the second year of university, with a major in math (80% of the courses). In the beginning, I was a bit lost, because I didn't have some basics. I struggled with the new concepts.
Luckily, I've met a student who is today my best friend. We studied together (not so much, don't worry lol!) and he explained me things I didn't understand. Actually, I had the intuitions, and he finished the working. That was a good combination And my intuitions and this combination were probably the things that prevented me from drawning.
At the same time, I started attending math forums. In a first time in order to ask questions, to clarify some stuff. And then, I was curious, I started reading the others' questions. Then I started replying to them. Oh sure, it was only basic or high school stuff. But it really helped me develop my reflexes and intuitions in maths, aside the stuff I was doing at the university.
Then I attended more math forums (that's bad lol!), replying to threads, to questions.
I didn't even notice I was replying to questions that were more difficult than in the beginning.

Well, finally, in my first semester of the second year, I got a very good average mark. Though there were easy subjects. The second semester was not as good, but very correct. Now, I'm finishing my third year, and it goes quite well. Though I don't always learn seriously and sometimes take this bad habit of relying on my ability to solve problems.

What I wanted to say is that if you're struggling now, who knows how tomorrow will be ? You just need to have a brain wave. Or something that stimulates your sleeping math skills lol!
I may not have put this in form, but I really mean it. You need to get started.

I'm aware you're an adult and probably don't have enough spare time to spend helping people in maths. But maybe you should try answering some math questions. Even they're basic. Then, be curious enough to look at more complicated things, that relate to what you're learning in a first time, then that use things you've learnt (and understood). Open your mind to maths
Also, read different sources, which is quite easy on the internet. This may provide you a different point of view. Many times, my best friend explained to me things the teacher said, in a different way. And sometimes, it was a very efficient way to understand...


Sorry if I'm messy, or if I talked too much about myself lol! I'm just trying to help you get some confidence...

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I can't stress how crucial it is to find difference reference on same topic, I was not very good with mathematical reading, struggle with the symbols and theorem and the relation between them. Sometimes, you might not understand how the theorem is stated in this lecture notes or textbook, but you'll find that you can be comfortable with it if it's stated in another way in another textbook.

But, now, i am doing some revise during my holiday, I am beginning to see more of what the theory is trying to say. And, don't get freak out if you have to read several times to understands, because most of us really need to do that ( except for some brilliant mathematical minds ). Also, a lot of people always said I can't understand this or that theorem, it 's often down to a lack of skill in reading and understanding. It's about understanding and making clear the concept, and then extract the useful properties and see how it relates to another theorem. ( this is quite similiar to philosophy, which explains why early mathematicians are at the same time a brilliant philosopher )

Also, try to find the rating of the suggested textbook by your lecturer in your course in Amazon.com. Some of the textbook maybe quite badly written or is simply too deep, and in this inctance it'll usually have lower rating, check out it's comment, some of it's reviewer will recommend another better book, where you'll gain some better understanding of a subject in a faster way.

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Oh and by the way, Did you take a course in foundations of mathematics or anything similiar of that sort, which involves math logic, basic set theory, relations, proof method ???? they are a must know if you want to obtain higher mathematics knowledge.

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Thank you both for the thoughts. I am constantly looking up various videos on the internet (what a great tool - again, this was never an option when I was in school.)

I find sometimes I hear the lecture or read the book and just think "What.. the... heck? I have no idea what the heck this means", but I proceed with sample problems and problem solving and videos about problem solving, and AFTER I do several problems if I go back and re-read or re-watch the lecture it's not quite as Greek to me.

Pho - I took a "Mathematics for Liberal Arts Majors" in college that primarily dealt with logic (minimal number crunching or problem solving.) Also my math courses in high school, I've come to realize, were what some high schools call "honors", and our Algebra II/Trig is what some schools call "Precalculus". We did almost nothing but proofs in Geometry, and geometry was my favorite math subject, so I do have a basic understanding of that. I did some C programming as a hobby, which gave me a little more insight into functions and their purpose.

For the degree I am thinking of seeking (rather *exploring the possibility of), I will need 5 math courses: The series of 3 Calculus courses, Linear Algebra, and Differential Equations. And then of course, I'm sure mathematics will be a large part of the science coursework as well.

Thats exactly the same as me! Did a different degree for a while, changed to maths, straight into second year. Totally lost! Had 6 resits that year... That summer was pretty grim.

But i got my head down and now I'm surely going to be getting a 1st for my degree (dont know what the equivalent is outside of UK, A, A*?)


But anyway...

Things ive found have really helped me is to look through these forums and find questions that ive not really seen before and then try and solve them through my own research. You remember things really well if you've actually learned them yourself rather than being taught them.

Also, apparently if you teach someone a topic you have an 80% higher chance of remembering it. So find someone, anyone, doesnt have to be someone off your course and tell them what your doing and explain things to them. Putting things in your own words helps them stay in your mind.

And one final thing! What I did this year is I arranged some parts of my course into talks and then practiced them a few times and i found that after an hour or two i had perfectly memorized everything i was talking about.

Good luck.