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Gil

Options after Differential Equations

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I know we have a few mathematicians and mathematically inclined parents on this board so I'm wondering if anyone can recommend a good sequence on applied mathematics for students who have completed calculus and differential equations.

 

I know that engineering students often have to take a couple semesters of E-Math or Engineering Mathematics, but what I don't know is what they covered or what texts they used, if they used one and I can't seem to find much on Amazon and those books I do find, I have no idea of knowing if they're good or not.

 

I want to save Numerical Analysis/Mathematical Modeling for after they have some competency programming and I've never really gotten them to be interested in Stats/Probability so I don't want to go to a full course on Stats just yet.

 

Any suggestions for a text on Applied Mathematics?

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We've done some discrete math, but it's been a while. Honestly, I'm scared of teaching--and especially grading proofs. Which is honestly a part of the reason that I'd really like a year/course of math that's heavy on applications. The bit of proofs we've done through discrete and calculus have shown me where my limits are. (Haha. That's a calculus joke.)

 

I guess we can do Linear Algebra, but are there any specific recommendations for a text? But surely there are tons of books out there for Applied Mathematics or Mathematics for Finance or Mathematics for Engineers and I'm missing them right? Right?

 

 

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We've done some discrete math, but it's been a while. Honestly, I'm scared of teaching--and especially grading proofs. Which is honestly a part of the reason that I'd really like a year/course of math that's heavy on applications. The bit of proofs we've done through discrete and calculus have shown me where my limits are. (Haha. That's a calculus joke.)

 

I guess we can do Linear Algebra, but are there any specific recommendations for a text? But surely there are tons of books out there for Applied Mathematics or Mathematics for Finance or Mathematics for Engineers and I'm missing them right? Right?

Some Engineering colleges have a Linear Algebra course that leans toward "application" versus one that a Math major would take.

They would probably be different texts

 

Maybe someone here can recommend some to look at it.

There are a few free "Open source" type texts - I can look them up and post those links if desired.

 

Mark

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Yes please.

 

Any help, ideas, links or leads that anyone can give is greatly appreciated. I don't have a solid plan of where to go from here.

I am NOT a mathematician, but definitely want to keep them interested and want to keep exposing them to interesting mathematical things, but also don't want to totally drop the ball on other things, you know.

 

I'm out of my depth with many of these things when it comes to evaluating the quality of resources too, so if anyone wants to point me at "vetted" resources, then please do. Bonus points if they are available on line for the cost of printing.

Edited by Gil

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Gil! Welcome back! 

 

Have you seen kiana's link in the giant math thread? There will likely be something there you can use (kiana knows her stuff!). Here it is: 

 

Posted by kiana 16 January 2018 - 04:22 PM

Free textbooks in many subjects, including math: https://open.umn.edu/opentextbooks/

Most have reviews. 

 

It includes pre-algebra, elementary algebra, elementary geometry, intermediate algebra, college algebra, precalculus, calculus, multivariable calculus, linear algebra, discrete mathematics, finite mathematics, elementary statistics, math for liberal arts, differential equations, introduction to proofs, abstract algebra (one or two semesters), number theory, probability, combinatorics, college geometry (Euclidean plane one, the other one is HS), real analysis (one or two semesters), data structures and algorithms, linear regression/programming

 

I will draw specific attention to: 

Math in Society, a Math for Liberal Arts class that would be an excellent 4th credit for a struggling or uninterested student, and do equally well for supplemental material for a bright younger student. 

Open Logic Project, rigorous but non-mathematical, aimed at students in the humanities. 

Advanced Problems in Mathematics, which looks like a collection of challenging problems that would be a fine supplement for any student eager for more. Intended to be for those taking examinations at Cambridge, so some problems may rely on A level material, which includes calculus. 

Algebra and Trigonometry, which is a college algebra/trig textbook that includes significant review in the first two chapters, ideal for someone who's forgotten a lot. 

Calculus for the Life Sciences I and II, which look ideal as a first exposure for someone more interested in those areas. 

Proofs and Concepts, designed for undergraduates but suitable for mathematically mature high school students as well. 

OpenIntro Statistics, a more advanced text that uses some calculus. 

 

 

 

Edited by Emerald Stoker

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What about some of the classes on mit's OCW?

 

Linear algebra is there (strang's book has a good reputation and he is the teacher -- the text includes enough applications that cornell uses it for their "linear algebra with applications" class). There's also "complex variables with applications", that has a prerequisite of differential equations. Those would give you a syllabus and assignments as well, which would be nice to have. Chaos theory is another undergrad class that actually *uses* diffeq, but theirs has a prerequisite of electricity and magnetism. 

 

There's also this free textbook that I'm looking at myself (but haven't previewed): https://aimath.org/textbooks/approved-textbooks/hitchman/ -- prerequisite of multivariable calculus. 

 

I haven't specifically reviewed the textbooks in the thread that emerald stoker linked, but there's a fair number of applied math textbooks there -- most are more probability/stats or discrete math textbooks. Finite math has a fair amount of linear algebra in it (a lot of duplicate content) and it might be an interesting way to head towards probability. Their book also has a game theory chapter, which I always found fascinating -- economists use it a lot. 

 

I also recommend you work on proofs just for yourself ;)

 

Edit: Also, as long as we're thinking applications of mathematics, it would definitely highlight them to go do a mathematically focused physics I and II class -- not sure what you're doing for science. 

 

Another edit: Stumbled on this this morning -- https://www.edx.org/course/differential-equations-linear-algebra-and-nxn-systems-of-differential-equations -- teaches some linear algebra and immediately uses it to solve systems of differential equations. Nice combination of what you've just done (assuming you haven't integrated this into your DE class)

Edited by kiana
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Wow, as always, the hive pulls through for me. So I want to give a Thank You* to everyone for your help with the various leads and links. 

I'll be combing through the table of contents and pouring over the books recommended to try and figure out the next move.

 

 

 

Got a lot to mull over now and plenty to chew on for a bit...

 

 

*Get it? A big thank you. Haha.

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