- #1
Aufbau
- 12
- 0
Hello all,
I feel as though I never learned mathematics the right way which severely impacted me from pursuing other science/math careers involving higher mathematics. I feel as though I need to approach mathematics from a proof based manner in order to properly learn. The way that mathematics is taught in the public school system is very memorization based to an extent. However, I am trying to mitigate this effect and re-learn everything I was ever taught (sciences too) in a more rigorous format. So far I have Spivak for Calculus I and II along with Courant Differential and Integral Calculus volumes I and II. For Multivariable Calculus I will be using Shifrin's Multivariable Calculus with linear algebra. Further I will be using Ross and another text for differential equations and later Real Analysis by Ireland and Artin for abstract algebra as well as a discrete mathematics-Lovatz. I wanted to use Feller for Statistics and a few other mathematics texts.
In addition, I will be starting my high school mathematics sequence over again (i.e., starting from algebra). I thought that starting out with number theory along with algebra followed by geometry and algebra II and finally with precalculus. Then I figured my math would be strong enough to get into Spivak and the others. I am not sure where to fit discrete math in with the other mathematics courses. The high school math list is as follows:
Modern School Mathematics Geometry-Jurgensen
Modern Algebra and Trigonometry (Book 2) Structure and Method-Dolciani
Modern Algebra Structure and Method (Book 1)- Dolciani
Modern Introductory Analysis-Dolciani
College Algebra-Charles H. Lehmann
Analytic Geometry by Steen and Ballou (3rd Edition)
We used the Holt, Rinehart, Winston series I believe for every math class I ever took with the exception of college and everyone knows that the Reform Calculus books aren't that great.
-I have noticed that working only difficult problems and taking time on those is better than working a ton of easy problems because the extremely difficult ones test your knowledge and ability to apply/synthesize the material.
Any commentary would be greatly appreciated. What I am basically asking is whether or not this approach is feasible and what are the flaws you currently see in it? What are some improvements that could be made?
Thank you-
I feel as though I never learned mathematics the right way which severely impacted me from pursuing other science/math careers involving higher mathematics. I feel as though I need to approach mathematics from a proof based manner in order to properly learn. The way that mathematics is taught in the public school system is very memorization based to an extent. However, I am trying to mitigate this effect and re-learn everything I was ever taught (sciences too) in a more rigorous format. So far I have Spivak for Calculus I and II along with Courant Differential and Integral Calculus volumes I and II. For Multivariable Calculus I will be using Shifrin's Multivariable Calculus with linear algebra. Further I will be using Ross and another text for differential equations and later Real Analysis by Ireland and Artin for abstract algebra as well as a discrete mathematics-Lovatz. I wanted to use Feller for Statistics and a few other mathematics texts.
In addition, I will be starting my high school mathematics sequence over again (i.e., starting from algebra). I thought that starting out with number theory along with algebra followed by geometry and algebra II and finally with precalculus. Then I figured my math would be strong enough to get into Spivak and the others. I am not sure where to fit discrete math in with the other mathematics courses. The high school math list is as follows:
Modern School Mathematics Geometry-Jurgensen
Modern Algebra and Trigonometry (Book 2) Structure and Method-Dolciani
Modern Algebra Structure and Method (Book 1)- Dolciani
Modern Introductory Analysis-Dolciani
College Algebra-Charles H. Lehmann
Analytic Geometry by Steen and Ballou (3rd Edition)
We used the Holt, Rinehart, Winston series I believe for every math class I ever took with the exception of college and everyone knows that the Reform Calculus books aren't that great.
-I have noticed that working only difficult problems and taking time on those is better than working a ton of easy problems because the extremely difficult ones test your knowledge and ability to apply/synthesize the material.
Any commentary would be greatly appreciated. What I am basically asking is whether or not this approach is feasible and what are the flaws you currently see in it? What are some improvements that could be made?
Thank you-
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