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*This is kind of a long read and it's just asking for advice. If you just feel like answering quickly, skip to the last paragraph or two for a summarized version*
At the end of my fourth year in high school, I was unsure what I wanted to take in University, so I went back for a fifth year. At the end of that, I decided on Psychology, as I have always found the brain and the way it works very intriguing. So that is how I came to choose Psychology as a major.
However, I also really enjoy Math. I like solving equations and especially like trying to figure out really complex or difficult questions; it's just fun for me. I live in Ontario, Canada and if your unaware of how schooling works here, it goes like so. When you are choosing the mandatory courses, (English, Math, Science, French (for our first high school year) and such) you are given a choose between applied or academic. For example, in Gr. 9, you can choose to take applied English or academic English. The difference is that applied English usually cuts out a portion of the curriculum (usually the most complex or hardest part) and lengthens the rest of the course, so it's just a slower and dumbed down version of academic English. Also in Canada, there are distinguishable differences from College or University. Colleges are where you go to learn a trade or learn jobs that are more hands on, (technicians, electricians, plumbers, cops and the like) while University is a place of higher learning and almost always require a higher average for acceptance.
In Gr. 9, 10 and 11, I choose academic Math. I never payed too much attention and always did just enough to get by with a 50-60 average. The problem with Math is that if you don't pay attention, you can't just start trying to understand the concepts later on, because your foundation is all fucked up. That's what's happened with me. In Gr. 12 I actually became a good student and started to pay attention, but I was afraid I wouldn't be able to 'get' Math at this point, so I dropped down to applied Math. So my entire Gr. 12 year was spent doing applied Math; which I found very easy, it was essentially the same thing as Gr. 10 Mathematics. It was at this time that I realized that I really liked doing equations. It wasn't just because it was easy, I liked finding the hard questions in the book and trying to do them, it was like a challenge.
When I went back for my fifth year, I wanted to take a harder Math, but I wasn't sure what to take. I wanted to take a course that started fresh, where I didn't need any prior knowledge; so I choose Data Management. I talked to Micronesia and he said in the States it may be called Statistics. I'm not sure, but it was all about bell curves, standard deviation, percentages, n choose r, graphs and things like that. It was an academic course and I wound up with a 92% in it without much studying at all.
So my dilemma now is that I am in Psychology, which I enjoy, but I really feel like I should be doing something in Math. It's what I really like and what I want to do. I spoke with Micronesia and he said that everything he took in his post secondary education required a little bit of everything. Some algebra, calculus, data and such. Since I haven't taken any 'real' algebra or calculus classes (besides the gr. 12 applied course; which was easy, but very basic) I am afraid that if I take a University level math course now, I would fail, regardless if I really tried to understand it.
What I'd like from you all is if your a Math major or just informed about mathematics; for someone in my situation, who hasn't really had proper learning of algebra and calculus, what is some advice you can give me for next year, assuming I want to major in Mathematics. What I have thought of so far, is to try to convince my parents to let me take night classes during the summer and maybe do tutoring on the side for some money, in preparation for my 2nd year at University. That way I could brush up on my Math and try to learn what I missed from dropping down to applied.
Should I perhaps just take the course and study hard? Will that be enough?
Are the night courses a good idea/ choice?
Thanks for the help.
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One question, are you even allowed to take a 5th year in high school??
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buy an algebra / algebra II / trig / precalc / calc book and study on your own o__O
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On December 09 2008 12:29 il0seonpurpose wrote:
One question, are you even allowed to take a 5th year in high school??
Of course. If I said no, that would imply that I somehow tricked the school or that the entire thread was a lie. Quite a few students return for a fifth year. Usually they are just unsure of what to major in or what they want to do, so it's a way to stay busy and avoid getting a job for another year.
On December 09 2008 12:30 paper wrote:
buy an algebra / algebra II / trig / precalc / calc book and study on your own o__O
How effective is that though? Wouldn't learning this way be rather difficult without a teacher?
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math + psychology = computational neuroscience
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If you're going to be taking first year math courses you should be fine.
You're in Ontario (like me) so they just took calc out of highschools (pretty much) so the first year math courses shouldn't assume any calc.
Bear in mind that in later years of a pure math major things are completly different than highschool math. Its proofs and proofs  .
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motbob
United States12546 Posts
This is going to seem weird, but if you really enjoy solving problems, you should give physics a try.
If that's not an option, you should post the course descriptions of the introductory math courses at your University. We'd be able to help you out better if you did.
+ Show Spoiler +
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United States24698 Posts
One concern I have is this: If you haven't taken any serious math courses yet, it's hard to tell how much you will like them, and how hard they will be for you.
As an analogy: I really didn't know what upper level physics was like until I got there. I chose my major with only ap physics b under my belt. But my gut was right and my natural inclination towards physics made getting the degree manageable. It's a gamble, but worth it to try what you really want to do. Think about what the damage would be if you decided after a couple of semesters that it wasn't working out, and weigh your option.
Hopefully some Canadians can shed some light since they are more familiar with your system.
edit: Such as Zortch ^^
edit2: motbob I hate that expression so much hahaha
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im curious what your math was in high school. You say you know nothing about algebra, but you must have taken some algebra. Same goes with the other courses. Your undergrad courses are basically refreshers of high school for a few weeks, then they continue along the path. Once you get to the higher level some of the introduce new topics like Topology, Numerical Analysis, Advanced Calculus etc.
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On December 09 2008 12:33 talismania wrote:
math + psychology = computational neuroscience
I guess now is a good time to point out that for Canadians, Science is only a required course for Gr. 9 and Gr. 10. I took academic versions of both and then never touched it again. The thought of taking biology or chemistry scares the hell out of me. (I just check the courses description for neuroscience; it says I would be taking Biology and Chem.)
On December 09 2008 12:33 Zortch wrote:If you're going to be taking first year math courses you should be fine. You're in Ontario (like me) so they just took calc out of highschools (pretty much) so the first year math courses shouldn't assume any calc. Bear in mind that in later years of a pure math major things are completly different than highschool math. Its proofs and proofs .
Well that's a load off. Assuming what you said is accurate, maybe the first year I wouldn't have much trouble at all.
On December 09 2008 12:33 motbob wrote:This is going to seem weird, but if you really enjoy solving problems, you should give physics a try. If that's not an option, you should post the course descriptions of the introductory math courses at your University. We'd be able to help you out better if you did. + Show Spoiler +
Much like the first answer I gave, physics requires taking science courses like chemistry; which I haven't taken since Gr. 10 and I never payed much attention. I am really kicking myself for not preparing in high school.
On December 09 2008 12:34 micronesia wrote:
One concern I have is this: If you haven't taken any serious math courses yet, it's hard to tell how much you will like them, and how hard they will be for you.
As an analogy: I really didn't know what upper level physics was like until I got there. I chose my major with only ap physics b under my belt. But my gut was right and my natural inclination towards physics made getting the degree manageable. It's a gamble, but worth it to try what you really want to do. Think about what the damage would be if you decided after a couple of semesters that it wasn't working out, and weigh your option.
Well; I did take Statistics/ Data as a course in Gr. 12 and I did very well in it and I found it very fun, it was my favourite course. I don't know how relevant that is to other Maths, though.
On December 09 2008 12:39 FzeroXx wrote:
im curious what your math was in high school. You say you know nothing about algebra, but you must have taken some algebra. Same goes with the other courses. Your undergrad courses are basically refreshers of high school for a few weeks, then they continue along the path. Once you get to the higher level some of the introduce new topics like Topology, Numerical Analysis, Advanced Calculus etc.
I do know algebra, I just haven't taken it at a challenging level for quite some time. Like I said, the course I take in Gr.12 was an applied course (basically an easy version of math) and it was about as hard as my Gr.10 academic math, so I breezed through it no problem. I am just afraid I missed so much by not taking Gr.12 academic math.
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On December 09 2008 12:33 motbob wrote:This is going to seem weird, but if you really enjoy solving problems, you should give physics a try. If that's not an option, you should post the course descriptions of the introductory math courses at your University. We'd be able to help you out better if you did. + Show Spoiler +
A course description for some Math I would have to take for one of the programs are:
Calculus Concepts 1
Differential calculus with an emphasis on concepts and the use of both theory and computers to solve problems. Precalculus topics, limits, continuity and the intermediate value theorem, derivatives and differentiability, implicit differentiation, linear approximation, mean value theorem with proof and applications, max and min, related rates, curve sketching, l'Hospital's rule, antiderivatives, Riemann sums, FTC with proof, integration by substitution. Use of Maple.
Calculus Concepts 2
Integral calculus with emphasis on concepts, theory, and computers to solve problems. Further integration techniques. Applications to areas between curves, volumes, arc length and probabilities. Multivariable calculus: partial derivatives, optimization of functions of two variables. Sequences and series: convergence tests, Taylor and Maclaurin series and applications. Differential Equations: direction fields, separable equations, growth and decay, the logistic equation, linear equations. Use of Maple.
Linear Algebra 1
Introduction to finite dimensional real vector spaces; systems of linear equations: matrix operations and inverses, determinants. Vectors in R2 and R3: Dot product and norm, cross product, the geometry of lines and planes in R3; Euclidean n-space, linear transformations for Rn to Rm, complex numbers, selected applications and use of a computer algebra system.
Math & Integrated Computers
Exploration of ideas and problems in algebra differential equations and dynamical systems using computers. Topics include number theory, integers mod p, roots of equations, fractals, predator-prey models and the discrete logistic equation for popular growth.
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Corinthos
Canada1842 Posts
going to bring a pro to help you
edit - later tomorrow, he's studying for exams, and so should I!
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You'll be fine to take those classes I bet.
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United States3824 Posts
Why don't you minor in Mathematics?
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u won't like math.
but definitely try it in college and see if you do.
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On December 09 2008 12:59 cgrinker wrote:
Why don't you minor in Mathematics?
That is a definite choice at well. I should have said that I really feel like I need to be studying mathematics in some way. I really enjoy what I have had so far and I want it to be part of my studies.
On December 09 2008 13:00 Zalfor wrote:
u won't like math.
Haha, well thanks for clearing that up :S
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On December 09 2008 12:50 Corinthos wrote:
going to bring a pro to help you
edit - later tomorrow, he's studying for exams, and so should I!
:O a pro?
Yes, I am studying for Philosophy as well. Exam week is rough.
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what uni do you go too?
It's almost time for me to apply to uni's and I am a bit overwhelmed :o
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On December 09 2008 12:46 Salv wrote:Show nested quote +On December 09 2008 12:34 micronesia wrote:
One concern I have is this: If you haven't taken any serious math courses yet, it's hard to tell how much you will like them, and how hard they will be for you.
As an analogy: I really didn't know what upper level physics was like until I got there. I chose my major with only ap physics b under my belt. But my gut was right and my natural inclination towards physics made getting the degree manageable. It's a gamble, but worth it to try what you really want to do. Think about what the damage would be if you decided after a couple of semesters that it wasn't working out, and weigh your option.
Well; I did take Statistics/ Data as a course in Gr. 12 and I did very well in it and I found it very fun, it was my favourite course. I don't know how relevant that is to other Maths, though.
Statistics is a whole different beast from other math courses. It's really not that hard taking first year stuff and not knowing anything from highschool, dont sweat it. The important stuff is usually in appendixes from your text book too.
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infinity21
Canada6683 Posts
On December 09 2008 13:04 Salv wrote:Show nested quote +On December 09 2008 12:50 Corinthos wrote:
going to bring a pro to help you
edit - later tomorrow, he's studying for exams, and so should I! :O a pro? Yes, I am studying for Philosophy as well. Exam week is rough.
He apparently thinks I'm a pro =/
*sigh* I guess I'm committed now
I'll read over it and tell you whatever I can about math tomorrow night. Got 2 exams in less than 24 hours 
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On December 09 2008 12:31 Salv wrote:Show nested quote +On December 09 2008 12:29 il0seonpurpose wrote:
buy an algebra / algebra II / trig / precalc / calc book and study on your own o__O How effective is that though? Wouldn't learning this way be rather difficult without a teacher?
it is very important to have a good teacher. especially when you're in university, choosing professors is usually discouraged, but if you can sneak into a good lecture and learn a lot, your money (parent's money) is going somewhere useful.
however, in my opinion, a good textbook is often better than the average teacher/professor.
you can always count on your textbook being there (unless you lose it) and you can seek answers even if you don't exactly know what you're asking (table of contents, index, appendix, or just read the whole section) and usually you can tell right away whether your textbook has the help you're looking for or not, rather than a tutor giving you tips you already know or don't need, or even worse, faulty advice.
if your textbook doesn't have what you need, go get another one (or go to the library and search one up).
if you get pissed at your textbook not being able to help you the whole year, you can sell it to some unknowing noob out there. you can't do that with teachers 
i keep a collection of all my good textbooks. i think i have like, 16 now? they probably weigh almost as much as i do, lol
edit: btw, most high school textbooks (the ones they give to you for free use during the year) are usually not the top in quality. At the beginning of a new curriculum term, publishers race to get their books out the fastest and cheapest. Schools buy these right away for those reasons. More up to date curriculum = +1 reputation, even if your up to date isn't really up to date. Students get the short end of the stick.
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infinity21
Canada6683 Posts
Note: I'll tell you my experiences but I must tell you that it'll be skewed since I've been taking advanced calculus (but regular everything else).
I skimmed through this thread and I can tell you at least in the University of Waterloo, high school calculus courses are largely useless to the exception of data management (very useful for stats). If you know how to differentiate/integrate, that's great. If not, you can learn in a week.
If you enjoy doing math, take some courses as your elective 2nd year and consider a major switch if you really enjoy yourself. Speaking from my own experience, I didn't rely on too many concepts I learned from high school in order to do advanced level calculus (1-3). You need logic and an ability to understand abstract ideas, not some technique you learned in hs. Of course, a lot of regular calc classes will have computation elements to it but you can look up the proofs to the theorems you're applying in class in order to really get what's going on.
For my advanced calc 1 class, we started with the least upper bound property as the axiom for the course and proved the completeness theorem and the fundamental theorem of calculus without making any other assumption. Not a single thing I did in AP math in high school helped me learn these stuff.
I personally really enjoy linear algebra because everything makes sense and I can see the relationship between all these things. A lot of questions are mechanical number crunching but the theorems/proofs are quite fun and challenging at times. It requires you to know theorems, their concepts, tricks on proving little results, etc.
If you think you'll struggle, you can get a friend to help you explain the concepts. Profs are very useful in this regard as well. Professors are in general very nice people so you can ask for as much help as you want
I say you give it a try and see if you like it. I don't think not taking academic courses in high school will hurt you that much. It just means you'll have to put in a little bit more effort but if you like it and put in a lot of effort, there's no reason to get anything below 70%.
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infinity21
Canada6683 Posts
Oh wait, I was supposed to help you tomorrow night... oh well ;;
Let me know if you have any questions regarding university math lol
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Hi, I'm going to make my first post on Team Liquid giving you advice I have a BS (soon to have a MS) in Math, so I can at least let you know what I've seen.
It seems like you've already got some good advice from other people. You seem to be interested in things that could go in many directions: math, physics, CS, etc. "Problem solving" using mathematical skills is necessary in any science. A math degree will have more rigor and proofs than a science degree, though.
However, many science related degrees will require the same lower level math courses. So, go ahead and take the calculus and linear algebra courses. Go ahead and take other general requirement science courses. Talk to professors or advisors in each department whose classes interest you. Then decide. You can always change, too.
As far as preparing for college level math classes, I can tell you what I've seen in my semesters of teaching. A strong foundation in (High School level) algebra and trigonometry will help you immensely. Believe it or not, most calculus students don't make calculus mistakes, they make algebra mistakes. So, go back and study your algebra. Remember how to factor, and how to solve different types of equations. Trig is also very useful. If you don't test into the calculus classes right away, you'll might end up taking a "precalculus" course to prepare yourself. This is not a bad thing, or a 'remedial' course. It's going over the algebra and trig in case you're one of the many students who didn't have a strong foundation in HS.
If you have any more specific questions, feel free to ask, and I'll try and help.
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On December 09 2008 22:33 ninjafetus wrote:If you have any more specific questions, feel free to ask, and I'll try and help.
Why is your name ninjafetus? :O
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I really appreciate the help; especially Infinity & Ninja.
I think I will take some algebra and calculus courses next year as my electives and see how I do and how I like it. I will probably take some science courses as well, it will most likely take some work; especially on the science end. I did a little research and there is a night course available in the summer for students who want more prep. for University. I may take this, it's not many hours a week and I can balance that and a job quite easily.
Thanks everyone for the great advice.
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On December 09 2008 12:46 Salv wrote:Show nested quote +On December 09 2008 12:33 motbob wrote:This is going to seem weird, but if you really enjoy solving problems, you should give physics a try. If that's not an option, you should post the course descriptions of the introductory math courses at your University. We'd be able to help you out better if you did. + Show Spoiler + Much like the first answer I gave, physics requires taking science courses like chemistry; which I haven't taken since Gr. 10 and I never payed much attention. I am really kicking myself for not preparing in high school.
That's sad since studying physics is the closest you can come to studying math problem solving, you get a whole different view on math once you start applying it to something "real" instead of just "Solve this equation system" or "Derive the rotational volume of this function around the x-axis", its "Solve this electrical circuit system" (Becomes a series of equations) or "Calculate the centre of gravity of this object" (Becomes a volume integral).
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On December 10 2008 02:27 Klockan3 wrote:Show nested quote +On December 09 2008 12:46 Salv wrote:On December 09 2008 12:33 motbob wrote:This is going to seem weird, but if you really enjoy solving problems, you should give physics a try. If that's not an option, you should post the course descriptions of the introductory math courses at your University. We'd be able to help you out better if you did. + Show Spoiler + Much like the first answer I gave, physics requires taking science courses like chemistry; which I haven't taken since Gr. 10 and I never payed much attention. I am really kicking myself for not preparing in high school. That's sad since studying physics is the closest you can come to studying math problem solving, you get a whole different view on math once you start applying it to something "real" instead of just "Solve this equation system" or "Derive the rotational volume of this function around the x-axis", its "Solve this electrical circuit system" (Becomes a series of equations) or "Calculate the centre of gravity of this object" (Becomes a volume integral).
Maths and applied maths (aka science + engineering) are very different things thoughs. people usually like one or the other, not both.
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On December 10 2008 02:47 KlaCkoN wrote:Show nested quote +On December 10 2008 02:27 Klockan3 wrote:On December 09 2008 12:46 Salv wrote:On December 09 2008 12:33 motbob wrote:This is going to seem weird, but if you really enjoy solving problems, you should give physics a try. If that's not an option, you should post the course descriptions of the introductory math courses at your University. We'd be able to help you out better if you did. + Show Spoiler + Much like the first answer I gave, physics requires taking science courses like chemistry; which I haven't taken since Gr. 10 and I never payed much attention. I am really kicking myself for not preparing in high school. That's sad since studying physics is the closest you can come to studying math problem solving, you get a whole different view on math once you start applying it to something "real" instead of just "Solve this equation system" or "Derive the rotational volume of this function around the x-axis", its "Solve this electrical circuit system" (Becomes a series of equations) or "Calculate the centre of gravity of this object" (Becomes a volume integral). Maths and applied maths (aka science + engineering) are very different things thoughs. people usually like one or the other, not both.
Yes, of course I know that, I even study both kinds. The thing is though that the OP said that he liked the problem solving qualities of HS math and a real math degree is not much like that, its full of stringent proofs and you can't go much by your intuition at all.
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as a math major and tutor for my university,
i took the liberty of containing all there is to know about calculus in the following picture:
when i got done with calculus i was all like "THATS IT?!? WTF SOCIETY LIED TO ME. they were all like omg calculus"
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+ Show Spoiler +On January 07 2009 14:26 wanderer wrote:as a math major and tutor for my university, i took the liberty of containing all there is to know about calculus in the following picture: when i got done with calculus i was all like "THATS IT?!? WTF SOCIETY LIED TO ME. they were all like omg calculus"
Thats a copout imo, why did you not paint the 3d one???
Or the vector one?
Or the complex one?
Or the tensor one?
Or the functional one?
But yeah, that is roughly the only things you need to know for most non-math majors. The calculus most are taking is basic math.
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apparently math majors can make over 90k depending on the field they go into -_-
i had no idea
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