Proof based classes for biomathematics major?

[sunny79]

Would proof based classes like real analysis, abstract algebra etc be helpful to a biomath major. Currently, I am a math major in a good community college, almost on the verge of transferring to a 4 year institution. My goal is eventually to get into med school and pursue radiation oncology but I would also like to conduct research where my math background might be of some help to develop mathematical models in relation to cancer etc. So coming back to the point would the proof based classes be of any help?

 

[IGU]

Would proof based classes like real analysis, abstract algebra etc be helpful to a biomath major...

Statistics. It's all about statistics. Learn real analysis, including measure theory, and you can learn probability theory and theory of statistics. And yes, proof based or you're wasting your time -- that's how you actually understand the stuff. Then you'll be head and shoulders above your peers in developing models that actually work. Most medical researchers (and virtually all clinicians) are clueless about statistics. People in the field who understand statistics are golden.

 

[Charles Stark]

Real Analysis for sure. I'm a current Math Major and when I took Real Analysis it changed the way I look at the subject. It opens you up and makes you think about problems. I would also try to do an upper level statistics. I have a statistics depth and the upper level statistics and probability classes are more helpful to me than the lower level ones. With Probability I assume you would benefit from learning about Markov's Inequality and Exponential Distributions as it has practical applications to biomathematics.

 

[sunny79]

Here are the courses which I have to take for bio math based on the curriculum where I wish to transfer...

Calc 1 to Calc 3
Differential equations
Differential equations for bio
Discrete and probabilistic models in bio
Mathematical theory of statistics
Mathematical theory of probability
Linear Algebra
Discrete Math

Electives...
Numerical Analysis
Probability 2 ( grad level course )
Graph theory
Combinatorics
Partial differential equations

 

[IGU]

Mathematical theory of statistics
Mathematical theory of probability

Yup. But not proof based, right? Doing these classes will get you some of the how but without really understanding the why. You need measure theory to do them right, and for that you need real analysis. Of course you don't really need them if you don't mind being like everybody else...

When you are working with new models in science you can say "Well, this is pretty much like this other problem over there so we can do similar things and it will work." but there are always simplifications and approximations that render such reasoning iffy. Unless you understand what you are doing all the way back to first principles you can't know if it's valid. Gaining the mathematical skills necessary for that will be repaid over and over.

 

[Charles Stark]

I think taking Real Analysis in addition to those sounds just fine. That list looks yummy.

Numerical analysis is fun if you like the challenge of programming (if that's how your particular section is taught.)
All of those have great applications to what you're wanting to do. Is the option of Mathematical Modeling available where you're at? I have taken it before and it has helped me tremendously with modeling. In it I learned about the process of building models that fit specific problems. It used numerical analysis, stats, probability, linear algebra and calculus depending on the problem. If they offer something like that I would recommend it.

 

[sunny79]

Thanks for the replies...I shall be taking proof based classes too. After all what's the point of being a math major without classes like real analysis, right?