If you know anything about these math courses:

[SparklyUnicorn]

MAT210   Discrete Structures: Logic & Proof

This course provides an introduction to the non-continuous side of mathematics. The course focuses on techniques of mathematical proof including mathematical induction, direct proof,indirect proof, and proof by contradiction. Topics include relations and functions, symbolic logic and predicate calculus, number thoery, combinatorial methods as well as an introduction to graph theory.

PR: MAT 180 Spring only

 

MAT222   Ordn Differential Equations

This course provides an introduction to ordinary differential equations. The course includes linear differential equations, systems of differential equations, series solutions, boundary value problems, existence theorems, Laplace transforms and applications to the sciences.

PR: MAT 181

 

These are my only two options for next semester (unless I go to the uni and at this point I'd prefer not to because it's more expensive, further away, and I still am homeschooling 2 kids so time is an issue). 

 

Not sure which of these courses I should take.  I'm leaning more towards the MAT210.  What's it like if you happen to know?  Why might I choose one course over another?  I currently have no future plans, and this is just for personal interest. 

 

[almondbutterandjelly]

I hated them both.  Discrete Structures teaches how to write proofs.  Ordinary Differential Equations teaches how to solve for fifth derivatives and stuff like that.  You need to have a really good teacher for either of them.  At my school, both were required for a math degree.  I would say Discrete Structures was most helpful, because of the proof instruction, which I later used in Analysis and Modern Algebra courses.

[4KookieKids]

 

MAT210   Discrete Structures: Logic & Proof

This course provides an introduction to the non-continuous side of mathematics. The course focuses on techniques of mathematical proof including mathematical induction, direct proof,indirect proof, and proof by contradiction. Topics include relations and functions, symbolic logic and predicate calculus, number thoery, combinatorial methods as well as an introduction to graph theory.

PR: MAT 180 Spring only

 

MAT222   Ordn Differential Equations

This course provides an introduction to ordinary differential equations. The course includes linear differential equations, systems of differential equations, series solutions, boundary value problems, existence theorems, Laplace transforms and applications to the sciences.

PR: MAT 181

 

These are my only two options for next semester (unless I go to the uni and at this point I'd prefer not to because it's more expensive, further away, and I still am homeschooling 2 kids so time is an issue). 

 

Not sure which of these courses I should take.  I'm leaning more towards the MAT210.  What's it like if you happen to know?  Why might I choose one course over another?  I currently have no future plans, and this is just for personal interest. 

 

 

Well, it may depend on the person. Personally, 210 sounds a lot like my first math class that made me LOVE math. Super fun (and also, super accessible -when taught correctly - even to elementary aged students), and lots of really new, fun ideas where you need creativity and open mind to approach things in new ways. But you have to be willing to veer away from procedural learning in favor of problem-solving. There will be precious few formulas to learn, and far fewer "only one way to do this problem" sort of techniques than in a standard math course up till now.

 

In my experience, something like 222 is mainly going to appeal to someone who enjoyed and excelled at calculus (I, II, and III). It was not a course I enjoyed because it is computation heavy. I enjoyed it far more than I did calc 2 or 3, granted, but that doesn't say very much. I know some folks who loved Diff Eq. I was just not one of them. I'm much more of a discreet sorta gal. :)

Edited October 5, 2017 by 4kookiekids

[SparklyUnicorn]

I'm enjoying calculus quite a bit.  But 210 sounds very different and interesting.

 

Maybe I should take Calc 3 before 222 though (it's not required).  Calc 3 isn't being offered in the spring so that's not an option. 

[regentrude]

I loved differential equations. But I would recommend completing calc 3 first. 

The techniques are elegant, sometimes it's a bit of a puzzle, and there are tons of applications.

 

While I'd find discrete math itself interesting, the course sounds like it could be dry. Proofs are great, but an entire semester "focused on technique of mathematical proof" may be too much.

 

 

 

Edited October 5, 2017 by regentrude

[SparklyUnicorn]

I loved differential equations. But I would recommend completing calc 3 first. 

The techniques are elegant, sometimes it's a bit of a puzzle, and there are tons of applications.

 

While I'd find discrete math itself interesting, the course sounds like it could be dry. Proofs are great, but an entire semester "focused on technique of mathematical proof" may be too much.

 

That's what it feels like to me.  Puzzles.  I like that part.  I think the one and only thing I don't enjoy is drawing graphs.  I can read the graphs and use the graphs and blah blah.  But physically drawing those damn things.  I think she had us draw 10 graphs on that damn test.  Good grief.  It was a bit much. 

[kiana]

The discrete structures course at my undergrad was what made me change my major to math. The differential equations class was very similar to calculus -- focused on applications -- but the discrete class was more like all of the puzzler parts of math that I loved. If you like solving math puzzles, well, it might be for you. 

[Arcadia]

That's what it feels like to me. Puzzles. I like that part. I think the one and only thing I don't enjoy is drawing graphs. I can read the graphs and use the graphs and blah blah. But physically drawing those damn things. I think she had us draw 10 graphs on that damn test. Good grief. It was a bit much.

Discrete structures is usually under the computer science prerequisites, while ordinary differential equations tends to be an engineering prerequisite.

 

Graph Theory is not graphs like the trigonometry kind. It is the Königsberg bridge problem kind of graph.

 

Link to MEP maths Graph Theory module so you can take a look

http://www.cimt.org.uk/projects/mepres/alevel/discrete_ch1.pdf

[4KookieKids]

I loved differential equations. But I would recommend completing calc 3 first. 

The techniques are elegant, sometimes it's a bit of a puzzle, and there are tons of applications.

 

While I'd find discrete math itself interesting, the course sounds like it could be dry. Proofs are great, but an entire semester "focused on technique of mathematical proof" may be too much.

 

Certainly, Diff Eq has more applications than discrete math. I agree that it would be best to have Calc 3 first, but Diff Eq really was "neater" than Calc 3.

 

Whether or not it's dry really depends on the instructor and the text. I think it can be very dry and boring. But by focusing on techniques of mathematical proof, I assume they mean stuff like learning induction (how if you can show one case is true, and you can show that each case follows from the one before, then it must be true in general), proof by contradiction (if the statement weren't true, life as we know it couldn't exist... lol), and learning how on earth you prove things when all you have to work with are dots and lines (does anyone remember the utilities problem? Three houses, three utility companies - can you connect each house to each utility without overlapping lines? Turns out the answer is no, but how do you KNOW?). Cool proofs for algebraic formulas that don't actually involve algebra - instead you set up a scenario and then count possible outcomes in more than one way (where one way of counting gives you one expression, and another way of counting a different one, but since you're counting the same things, you can conclude that your expressions must actually be equal.) I loved this part, because it really required you to think outside of the box! So there's really a lot of cool content here, and just a very different flavor than proofs in calculus, geometry, or any of the more applied or analytical branches of math.

[4KookieKids]

That's what it feels like to me.  Puzzles.  I like that part.  I think the one and only thing I don't enjoy is drawing graphs.  I can read the graphs and use the graphs and blah blah.  But physically drawing those damn things.  I think she had us draw 10 graphs on that damn test.  Good grief.  It was a bit much. 

 

Yes, totally different kind of graphs. In this context, a graph is just a set of dots and a set of lines connecting these dots however you'd like. :)

 

ETA if you imagine the utility problem I referenced above, you can imagine each of the houses and utilities just as dots, and then the problem is really just a question of if a certain "graph" (dots with certain lines between them) exists.

 

Edited October 5, 2017 by 4kookiekids

[regentrude]

 But by focusing on techniques of mathematical proof, I assume they mean stuff like learning induction (how if you can show one case is true, and you can show that each case follows from the one before, then it must be true in general), proof by contradiction (if the statement weren't true, life as we know it couldn't exist... lol), and learning how on earth you prove things when all you have to work with are dots and lines 

 

Slightly off topic related question:

so proof by induction being saved for a 200 level college class means this is not covered in high school?

 

I still remember our 11th grade math teacher (whom I could not stand) repeat in his annoying voice "If the k-th domino stone tips, then the (k+1)st domino stone tips..." Neat stuff.

[Arcadia]

Slightly off topic related question:

so proof by induction being saved for a 200 level college class means this is not covered in high school?

It is in Holt Algebra 2 chapter 11 (page 45 of link), proof by induction is definitely introduced in high school.

https://www.augusta.k12.va.us/cms/lib01/va01000173/centricity/domain/766/chap11.pdf

[kiana]

Slightly off topic related question:

so proof by induction being saved for a 200 level college class means this is not covered in high school?

 

I still remember our 11th grade math teacher (whom I could not stand) repeat in his annoying voice "If the k-th domino stone tips, then the (k+1)st domino stone tips..." Neat stuff.

 

hahahahahaha ... no.

 

It might be covered in some honors level classes somewhere. But many students, frankly, have never seen a proof other than a cursory exposure to cookie-cutter two-column "proofs" in geometry, if that. 

 

After all, proofs aren't something that you can assess with a standardized test, so they can't be good for anything. 

[4KookieKids]

Slightly off topic related question:

so proof by induction being saved for a 200 level college class means this is not covered in high school?

 

I still remember our 11th grade math teacher (whom I could not stand) repeat in his annoying voice "If the k-th domino stone tips, then the (k+1)st domino stone tips..." Neat stuff.

 

With few exceptions, that is correct. Most of my 300 level college students have never seen induction before. And they are math majors who, with few exceptions again, took calc in high school even.

[regentrude]

hahahahahaha ... no.

 

It might be covered in some honors level classes somewhere. But many students, frankly, have never seen a proof other than a cursory exposure to cookie-cutter two-column "proofs" in geometry, if that. 

 

After all, proofs aren't something that you can assess with a standardized test, so they can't be good for anything. 

 

 

With few exceptions, that is correct. Most of my 300 level college students have never seen induction before. And they are math majors who, with few exceptions again, took calc in high school even.

 

That is sad. But then, I am not surprised, because I see the results of what passes for high school math every semester with my college students.

:sad:

[4KookieKids]

That is sad. But then, I am not surprised, because I see the results of what passes for high school math every semester with my college students.

:sad:

Yes, it is very sad. Though honestly, I was even IN honors courses in high school (IB), and I didn't see induction until college. 

[regentrude]

Yes, it is very sad. Though honestly, I was even IN honors courses in high school (IB), and I didn't see induction until college. 

 

I remember that we used induction to prove sum expressions for series in school. How else would one do that?

And you'd have to cover sequences and series before calculus, to get to the idea of the limit, right?

[kiana]

I remember that we used induction to prove sum expressions for series in school. How else would one do that?

And you'd have to cover sequences and series before calculus, to get to the idea of the limit, right?

 

We can assume no prior knowledge whatsoever of sequences and series in calculus class. Limits are presented first intuitively and then with the epsilon-delta definition, although it is uncommon for a calculus 1 class to actually understand the second. While sequences are used (for example, to justify lim_{x \to 0+} /frac{1}{x}), the sequence with x = .1, .01, .001, ... will be shown, however, the formal terminology will not be. 

 

It is quite common to present high school students with formulas without deriving them. Many of them have told me that they have literally never seen a formula derived, but only presented for memorization. 

[4KookieKids]

I remember that we used induction to prove sum expressions for series in school. How else would one do that?

And you'd have to cover sequences and series before calculus, to get to the idea of the limit, right?

 

No, calculus in high school (I didn't actually take a class called "calculus", so I'm speaking of second hand knowledge from high school students I've tutored, college students I've taught, and currently the high school teachers I'm teaching) does not do epsilon-delta proofs of limits. In fact, I went to a smaller college, and didn't see epsilon delta proofs until after I finished calc 3 and was taking Real Analysis. Though I currently teach at a much larger university, and they do teach the concept of an epsilon-delta proof, but they don't require students to actually do it in calculus (it's saved for a later course).

 

Sequences and series are all done very intuitively up until much later. I'm not sure how it used to be, but this is definitely the common experience at this point.

[MarkT]

I loved Diffy Q - I agree it is like solving a puzzle 

 

What are you pursuing?

[SparklyUnicorn]

I loved Diffy Q - I agree it is like solving a puzzle 

 

What are you pursuing?

 

Fun and knowledge? :laugh:

 

I think ultimately I'll end up taking both.  Just wondering which I should start with. 

[daijobu]

If you want to get a taste of Discrete Math, there's a Great Courses class taught by a Harvey Mudd professor that I'm enjoying right now.  It has lots of proofs, but he also does a fair bit of problem solving.  As a bonus, he gives an excellent description (with a proof!) of RSA encryption.  

[SparklyUnicorn]

If you want to get a taste of Discrete Math, there's a Great Courses class taught by a Harvey Mudd professor that I'm enjoying right now.  It has lots of proofs, but he also does a fair bit of problem solving.  As a bonus, he gives an excellent description (with a proof!) of RSA encryption.  

 

ohhh I like him.  I have watched two of his other lecture series. 

 

Thanks!