How to build a solid foundation in mathematics????

So, I'm going back to school. I already have a B.S. in biochemistry but I've found out that junior scientists aren't really in any demand whatsoever. So, I want to study bioengineering and try to make myself more competitive. If I'm going to become a better scientist I need to know how to play around with sets, classes, categories, systems, whatever the nomenclature/method. That's where math is, hopefully, gonna save the day for me. I guess I need explicit definitions to better understand mathematics. Hopefully, I'm studying the right stuff?

Set theory

Set Theory (Stanford Encyclopedia of Philosophy)

Set theory alternatives

Alternative Axiomatic Set Theories (Stanford Encyclopedia of Philosophy)

Category theory

Category Theory (Stanford Encyclopedia of Philosophy)

I'm working on conceptualizing set theory with my current understanding of mathematics (I've taken Calculus II). I think I'm starting to understand first-order logic and higher-order logic? I've seen the Russian nesting doll analogies, fractals, and other examples of how math/logic is made heirarchical. Even though I'm encountering very explicit definitions for objects it seems that they are still recursively defined? Is that where ZFC is supposed to save the day? I guess I just need to keep reading more and more and play around with the concepts. I can see how a cartesian system becomes entirely unintelligible without explicit rules to build from. It's starting to make some sense I guess?

Re: How to build a solid foundation in mathematics????

Hey Big_A.

If you are doing engineering, then my advice would be to focus on the practical aspects of mathematics and learn more about applied mathematics than the pure variety.

This involves understanding how to program computers in a basic way (and more advanced for more complex analyses) and learning how to model real world phenomena and extract the important pieces of data out of your analyses.

You also have to be able to translate all your findings into really simple terms for the person who is using your data and they often won't know what the hell it is that you are doing in a technical sense.

The important thing for an applied mathematician (which includes to a large extent engineers and statisticians) is to put the math into context and not the other way around.

The pure mathematicians are the ones that make sure all the techniques and results are what they say they are: the applied people for the most part don't care about the intricacies: as long as the technique works and as long as you are meeting the assumptions and know what you are doing, then you can focus on what you are good at and what you are meant to do (engineering, advising, modeling etc).

Re: How to build a solid foundation in mathematics????

Quote:

Originally Posted by

**chiro** Hey Big_A.

If you are doing engineering, then my advice would be to focus on the practical aspects of mathematics and learn more about applied mathematics than the pure variety.

This involves understanding how to program computers in a basic way (and more advanced for more complex analyses) and learning how to model real world phenomena and extract the important pieces of data out of your analyses.

You also have to be able to translate all your findings into really simple terms for the person who is using your data and they often won't know what the hell it is that you are doing in a technical sense.

The important thing for an applied mathematician (which includes to a large extent engineers and statisticians) is to put the math into context and not the other way around.

The pure mathematicians are the ones that make sure all the techniques and results are what they say they are: the applied people for the most part don't care about the intricacies: as long as the technique works and as long as you are meeting the assumptions and know what you are doing, then you can focus on what you are good at and what you are meant to do (engineering, advising, modeling etc).

Definitely, I concur. I think I'm done with pure math, for now. Still, it was all good reading though. We are complex systems and having seen those explicit definitions a lot of ambiguity has been cleared for me. It will certainly help with understanding/conceptualizing. I'm disappointed I didn't get taught this stuff in high school. I guess I probably wouldn't have paid any attention. I would have thought it boring.

Anyways, thanks for the help. I can see how rich our language (spoken/written/mathematical) is.

Re: How to build a solid foundation in mathematics????

Quote:

Originally Posted by

**chiro** Hey Big_A.

If you are doing engineering, then my advice would be to focus on the practical aspects of mathematics and learn more about applied mathematics than the pure variety.

This involves understanding how to program computers in a basic way (and more advanced for more complex analyses) and learning how to model real world phenomena and extract the important pieces of data out of your analyses.

You also have to be able to translate all your findings into really simple terms for the person who is using your data and they often won't know what the hell it is that you are doing in a technical sense.

The important thing for an applied mathematician (which includes to a large extent engineers and statisticians) is to put the math into context and not the other way around.

The pure mathematicians are the ones that make sure all the techniques and results are what they say they are: the applied people for the most part don't care about the intricacies: as long as the technique works and as long as you are meeting the assumptions and know what you are doing, then you can focus on what you are good at and what you are meant to do (engineering, advising, modeling etc).

Totally agree with you buddy. Specially about the points you mention regarding applied mathematics. You should follow it Big_a

Re: How to build a solid foundation in mathematics????

Quote:

Originally Posted by

**boogey** Totally agree with you buddy. Specially about the points you mention regarding applied mathematics. You should follow it Big_a

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