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actually I decided I'm not gonna take a class this spring, but I'll try to fit discrete math next fall when I start college.
And thank you. It's because I exhausted the math courses my high school had to offer by sophomore year, and my math teacher encouraged me to enroll in college level courses starting junior year, so that's when it started.
I know a couple of profs who I talk to from time to time, but they're too busy with their own research so I mostly do things by myself.
Thanks for the help by the way. I'll probably ask you more questions in the future
It's a circuit analysis text designed for technology and non-EE engineering majors after they have studied E&M in their physics courses. Physics texts only scratch the surface on how to solve circuits. Circuit analysis texts covers additional methods in solving circuits and in greater depth. It's certainly allowed me to review everything from physics, since it's been 7 years since I took the physics sequence.
I'm really impressed with the types of courses you've taken so far. You've already accomplished a lot considering that you're a high school senior. Do you talk with the academic advisers at the university often? Those professors can really help out a lot with course planning and such.
Keep in touch. I'd be more than willing to give advice and talk about math and math-related topics in general. I've added you to my buddy list.
thanks you for the recommendations. The symbolic logic course looks interesting, and I'll definitely sign up for some sort of discrete math course for spring. I've taken AP macro and micro econ and I like econ in general, but I'm not sure if I'll have room for intermediate level econ for next year.
About the electromagnetic theory you're learning, are you ading a book from an engineering point of view or from a physicist's point of view?
I've been away from the computer the past couple of days. I'm actually teaching myself electric circuit theory beyond what I learned in physics. Electromagnetism is a very interesting subject. I'm sure you'll enjoy this area when you study physics at the college level. I joined the alumni association and I'm checking out textbooks from the library. So I've been teaching myself stuff and staying focused, which explains why I've been away from the computer.
At the graduate level, applied math also becomes more proof-based too. So I probably won't pursue a graduate degree in math. So if I pursue a grad degree, it would probably have to be in a related field. I'm thinking of going back to school and earning a second bachelor's in either economics or electrical engineering.
I want to make a few recommendations for you based on my experience:
1. Consider taking a Symbolic Logic course in the Philosophy department during your freshman year. It's essentially just another math class and it usually meets the General Education (GE) requirement for "Critical Thinking".
2. I recommend taking both a basic statistics and a discrete/finite math course before enrolling in calculus-based probability theory. Discrete Math gives you a deeper understanding of the combinatorics needed to study probability theory. Basic statistics allows you to brush up on the basics of probability and leaves you better prepared for the calculus-based probability course.
3. For the Social Science GE requirement, considering taking an economics class, since it's heavy in mathematical ideas and concepts. I'd consider taking macro before micro. It's good to understand the "big picture" with macro before studying micro.
To be honest, I'm still a high school senior ahaha, although I've started taking college level math last year (I know, I'm a nerd, but I just love math too much). I'm not taking classes this semester though.
So I'm entering college this fall, and I'm still at a crossroads between pure and applied. Both appeal to me at this point. I loved my number theory and analysis class. But applied math is just as fascinating.. I'm interested in working with computational methods and their applications, algorithms (numerical analysis), math modeling, all that jazz. Mathematical physics is also an option. Right now I just got the hang of MATLAB and I'm working on some programming with C++.
It seems like you're really passionate about math too, which is a rarity [ if not an anomaly ] in this forum. Did you pursue graduate studies?
PDE's are somewhat less computational and more difficult to solve compared to ODE's, but the emphasis on computations or proofs really depends on the professor and on the textbook that's being used for the class. Like when I took Complex Variables my professor didn't put any proofs on the tests. It was all functions, integrations, derivatives, residues, and series. So I did really well in that class. But some of my classmates who took Complex Variables with a different professor ended up doing a few proofs just like in a Real Analysis class along with the computational topics that I previously mentioned. So it basically all comes down to the professor that's teaching the class.
Schaum's Outlines are the best study guides for math classes. Those things can help out a lot. I recommend browsing through a Schaum's outlines for PDE's at the bookstore to get a good idea as to what the subject entails.
Does your school allow you to take those Advanced Math for Engineers courses as electives? Those courses cover stuff like complex variables and PDE's without much emphasis on proofs.
It's great to be talking to another math major here.
Linear Programming is a very fun class. It's basically an extension of Matrix Algebra, except you're dealing with inequalities instead of equations. I also liked Boolean Algebra and digital circuits. You work with a bunch of 0's and 1's. Calculus-based probability theory was also one of my favorites too.
Are there proofs too in courses like PDEs? Or is just mostly computational methods?
I've taken maths up to ODE's and I've taken real analysis and algebra and did pretty good on those.
Yeah, I did the applied math option over at Cal State LA. I graduated in Fall 2006.
There's a considerable difference between pure math and applied math, at least at the bachelor's degree level. I wasn't aware of such a difference until I first started taking upper division courses. Pure math courses are all about analyzing theorems/proofs, constructing your own proofs, and being tested on proofs. Applied math courses are more about mastering computational methods, solving word problems, and solving math-related problems in other fields such as economics, management, physics, engineering, etc. So applications and computations are the main focus for applied math. I find applied math to be a lot more interesting than pure math.
Math has always been my love. That's why I majored in it. But it's just the proofs that give me big headaches.
Did you major in computational math?