Is enrolling in a course for next semester wise if the topic....

[Eclair_de_XII]

of the course is very much related to one of the courses one is taking right now?

[Warning: Long post. Skip to the third paragraph for what you need to know.]

I ask this partially because I'm beginning to think that it feels like a hassle taking Partial Differential Equations right after learning about Ordinary Differential Equations (which is a much more interesting class, by the way). Maybe it's because my ODE class taught me more intensive techniques than my PDE class and covered more math concepts, though. Or maybe it's because of my PDE professor who moves through the material extremely slowly, covering proofs and examples that are ripped straight from the book. But I'm done ranting about my PDE class.

Anyway, I'm taking Elementary Probability and Statistics right now and am strongly opposed to the idea of taking a related course in the spring, Probabilistic Models in Biology. I took a look through the book that this course uses in my campus bookstore a few days ago. And it turns out that a good chunk of the course goes through the material in the Probability and Statistics course I'm taking right now, in addition to including some Linear Algebra and Differential Equations stuff I learned a while back. The book was Mathematical Methods in Biology, by the way.

As a math major aspiring to become an actuary, I can't help but think that I should be obligated to take as many courses related to probability as I can. At the same time, though, if I take a course that is very interrelated to a course I'm taking right now, I feel as though going through next semester's course will exhaust me and make me lose interest in the class very quickly. Additionally, I will be taking the more advanced probability and statistical inference classes next year, so for the lack of a better word, I kind of need a break from going through probability and statistics. I kind of want to learn something new.

I have three courses to choose from:

(1) Probabilistic Models in Biology
"Probabilistic mathematical modeling emphasizing models and tools used in the biological sciences. Topics include stochastic and Poisson processes, Markov models, estimation, Monte Carlo simulation and Ising models and Ising models. A computer lab may be taken concurrently." (pre-requisite: Calculus II)

(2) Introduction to the Theory of Numbers
"Congruences, quadratic residues, arithmetic functions, distribution of primes. Emphasis is on teaching theory and writing, not on computation." (pre-requisite: Proof-writing)

and

(3) Foundations of Euclidean Geometry.
"Axiomatic Euclidean geometry and introduction to the axiomatic method." (pre-requisite: Calculus III, and Proof-writing).

I'm leaning on Euclidean Geometry, but I'm looking for any second opinions you might have.

 

[Mark44]

of the course is very much related to one of the courses one is taking right now?

[Warning: Long post. Skip to the third paragraph for what you need to know.]

I ask this partially because I'm beginning to think that it feels like a hassle taking Partial Differential Equations right after learning about Ordinary Differential Equations (which is a much more interesting class, by the way). Maybe it's because my ODE class taught me more intensive techniques than my PDE class and covered more math concepts, though. Or maybe it's because of my PDE professor who moves through the material extremely slowly, covering proofs and examples that are ripped straight from the book. But I'm done ranting about my PDE class.

How do you know that PDE is more interesting or will cover more intensive techniques than ODE? You're comparing a class you've taken with one you haven't taken yet. PDE is quite a bit different from ODE. Many situations in real life lend themselves more to modelling with PDEs than to simpler functions of a single variable.

Anyway, I'm taking Elementary Probability and Statistics right now and am strongly opposed to the idea of taking a related course in the spring,

by "related course," I assume you're talking about the Probabalistic Models in Biology class that you mention below. The elementary class you have now is just that -- an elementary class. I don't know what will be covered in the Prob. Models class, but it's possible to get very much deeper into probability and statistics than what are normally covered in an intro class on Prob./Stats. For example, when I was in grad school, I took a year-long sequence in Mathematical Statistics, in addition to another grad-level class on probability that involved, among other things, Lebesgue measure.

Probabilistic Models in Biology. I took a look through the book that this course uses in my campus bookstore a few days ago. And it turns out that a good chunk of the course goes through the material in the Probability and Statistics course I'm taking right now, in addition to including some Linear Algebra and Differential Equations stuff I learned a while back. The book was Mathematical Methods in Biology, by the way.

As a math major aspiring to become an actuary, I can't help but think that I should be obligated to take as many courses related to probability as I can. At the same time, though, if I take a course that is very interrelated to a course I'm taking right now, I feel as though going through next semester's course will exhaust me and make me lose interest in the class very quickly. Additionally, I will be taking the more advanced probability and statistical inference classes next year, so for the lack of a better word, I kind of need a break from going through probability and statistics. I kind of want to learn something new.

I have three courses to choose from:

(1) Probabilistic Models in Biology
"Probabilistic mathematical modeling emphasizing models and tools used in the biological sciences. Topics include stochastic and Poisson processes, Markov models, estimation, Monte Carlo simulation and Ising models and Ising models. A computer lab may be taken concurrently." (pre-requisite: Calculus II)

(2) Introduction to the Theory of Numbers
"Congruences, quadratic residues, arithmetic functions, distribution of primes. Emphasis is on teaching theory and writing, not on computation." (pre-requisite: Proof-writing)

and

(3) Foundations of Euclidean Geometry.
"Axiomatic Euclidean geometry and introduction to the axiomatic method." (pre-requisite: Calculus III, and Proof-writing).

I'm leaning on Euclidean Geometry, but I'm looking for any second opinions you might have.

If it were me, the Euclidean Geometry class would be my last choice, but that's just me. My top choice would be either the PDE class or the Prob. Models in Biology, with the Number Theory class being up there pretty close. For the PDE class, is the professor you mentioned the only person who teaches this class? A different instructor might present the material in a different way.

 

[MidgetDwarf]

I would choose the PDE course. However, the Probabilistic models in Biology would be the "better choice," if you like Biology. If your Prob and Stat course was proof based, it would be nice to see its application. Maybe you can get a deeper understanding of the theorems you worked with. However, I feel that PDE, at the introduction level, is a course you can easily self study.

If you are not into "pure math", then you may find the number theory course a nightmare... It may not align with your interesest or be apparently useful for your needs...

 

[Eclair_de_XII]

How do you know that PDE is more interesting or will cover more intensive techniques than ODE? You're comparing a class you've taken with one you haven't taken yet. PDE is quite a bit different from ODE. Many situations in real life lend themselves more to modelling with PDEs than to simpler functions of a single variable.

I would choose the PDE course.

I'll consider it. But it's not really top priority at the moment, I think. I have a friend who says that the instructor takes four whole weeks to move through one chapter; he told me that the instructor copies his lectures straight from the book. The instructor he's taking right now is teaching next semester's PDE course, too, so I'm a bit ambivalent about taking it and seeing what the course is about firsthand.

The elementary class you have now is just that -- an elementary class. I don't know what will be covered in the Prob. Models class, but it's possible to get very much deeper into probability and statistics than what are normally covered in an intro class on Prob./Stats.

The general syllabus for the Probabilistic Models in Biology looks something like: http://math.hawaii.edu/home/syllabi/syllabus-305.pdf. But I do suppose that I cannot know exactly what's being taught in a class by its syllabus alone.

If your Prob and Stat course was proof based, it would be nice to see its application.

The probability and statistics course I'm taking was almost entirely calculation-based. While I do want to apply it to something useful, I don't want to get burnt out by taking three probability/statistics courses three semesters in a row; if that's even possible... Maybe I'm worrying over nothing.

 

[MidgetDwarf]

I'll consider it. But it's not really top priority at the moment, I think. I have a friend who says that the instructor takes four whole weeks to move through one chapter; he told me that the instructor copies his lectures straight from the book. The instructor he's taking right now is teaching next semester's PDE course, too, so I'm a bit ambivalent about taking it and seeing what the course is about firsthand.
The general syllabus for the Probabilistic Models in Biology looks something like: http://math.hawaii.edu/home/syllabi/syllabus-305.pdf. But I do suppose that I cannot know exactly what's being taught in a class by its syllabus alone.
The probability and statistics course I'm taking was almost entirely calculation-based. While I do want to apply it to something useful, I don't want to get burnt out by taking three probability/statistics courses three semesters in a row; if that's even possible... Maybe I'm worrying over nothing.

Look at the book Probability and Statistics by Degroot. It has proofs in there. This is the book I am going to use next semester for a Theory of Probability course next semester. I am dual majoring in physics and pure math. It seems to fit my needs. I will later will take a statistical mechanics course.

Then, I would try the number theory course. It may be fun. You can maybe do a directed study if you find a professor.

How is your proof writing ability?

 

[Eclair_de_XII]

How is your proof writing ability?

It's decent, but nothing special.

 

[MidgetDwarf]

It's decent, but nothing special.

Graph Theory can also be fun.

 

[Eclair_de_XII]

I think I'm going to go with the Probabilistic Models in Biology class, after all.

I should maybe get used to using probability theory more often if I continue in my current career path.