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#1 Origin  Icon User is offline

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Mathematics Question ... AND ... Computer Science Masters Question

Posted 10 September 2013 - 09:51 AM

All -

I am currently a CPA and am returning for a Masters in Computer Science at age thirty-nine. I will not get into all of the reasons for this decision but suffice it to say that quality of life is primarily determined by subjective factors; not objective factors. Money does not buy happiness but following one's heart does.

The question I would like to pose to the room is this: if you had three months to learn/refresh in the topics of Precalculus Algebra and Precalculus Trigonometry prior to taking a single CLEP test for those two courses (to place in Calculus I), what is the most efficient and effective way to study assuming you had forty hours each week over the three month period to prepare?

My thought is obviously to study a college level text book on the topic and then maybe take a week and review a CLEP study guide prior to the actual test. With that in mind, I am concerned that not all textbooks are equivalent and that some may emphasize certain mathematical topics at the expense of others, and that in turn may lead to my being less prepared for the CLEP exam.

I must also emphasize that while I have already studied mathematics through Calculus I, these studies have been several years back, and in the case of Calculus I were business oriented (less difficult). Soooo .... given the importance that a solid mathematics education has in computer science - and, also considering that I am interested in pure mathematics anyway - it seems best to take a slower, methodical and well studied approach in preparation for the CLEP exam.

My second question is related to the viability of a Masters in Computer Forensics and Security Management over a traditional Masters in Computer Science program.

My goal in one year's computer science prerequisites and another two year's master's course work is three-fold: A) to provide an educational framework that will act as a foundation to build a portfolio of programs; B) to obtain an "interview ticket" at larger software companies (e.g., a company that has interesting projects that pay well); and, C) to create a "new life" wherein I can spend my time each day doing something I am truly interested in. In an ideal, parallel universe, all material needs would be met and therefore there would be no need to consider monetization of one's passion, but in this fallen, decaying world one must always bear in mind the economic ramification of all decisions; thus, sadly, I must, state parts A & B. My real reason for going back to school is simply because I love learning and am absolutely fascinated with mathematics, and as an application of mathematics, making computers do interesting things.

Bearing in mind the monetary aspect, which master's program would offer the most versatility and marketability? I would think, from the outside looking in, that the Masters in Computer Science would have the most job opportunities, and job flexibility in terms of availability in more geographic places and/or ability to work from home, whereas the Masters in Computer Forensics and Security Management would have more limited job opportunities and flexibility due to there being fewer potential employers.

As a final thought, my feeling is that the Masters in Computer Science would be the better choice simply because I know I like mathematics and programming; however, the Masters in Computer Forensics and Security Management is honestly a better (quicker) fit with my background as accountants are often used in the areas of IT Auditing and Forensic Accounting (neither of which I have performed, but I do have the general accounting skill set). Also, having a CPA with the Masters in Computer Forensics and Security Management would be a fairly rare pedigree which could make me very attractive to the job market. Nonetheless, I am more of a nerd than a business guy, so although that makes more sense based on my work and educational experience, it may simply not fit with "who I am."

Okay, guys and gals ... I know I ran a wee long, but thank you all who took time to skim this far. Any thoughts or opinions are greatly appreciated!

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Replies To: Mathematics Question ... AND ... Computer Science Masters Question

#2 modi123_1  Icon User is offline

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Re: Mathematics Question ... AND ... Computer Science Masters Question

Posted 10 September 2013 - 10:02 AM

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the viability of a Masters in Computer Forensics and Security Management over a traditional Masters in Computer Science program.
[...]
which master's program would offer the most versatility and marketability?

One would think that is an easy question - do you want to head into Computer Forensics or not?

Quote

what is the most efficient and effective way to study assuming you had forty hours each week over the three month period to prepare?

My thought is obviously to study a college level text book on the topic and then maybe take a week and review a CLEP study guide prior to the actual test.


With zero knowledge about you, your study habits, what you know, or what you don't questions like "the most efficient" is relative up to you. When I studied for the GRE I picked up multiple test prep books, and a book of nothing but practice test. I found my study guide via an amalgamation of those test prep books, and the faux tests helped ID weak spots.
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Re: Mathematics Question ... AND ... Computer Science Masters Question

Posted 10 September 2013 - 10:08 AM

View Postmodi123_1, on 10 September 2013 - 10:02 AM, said:

Quote

the viability of a Masters in Computer Forensics and Security Management over a traditional Masters in Computer Science program.
[...]
which master's program would offer the most versatility and marketability?

One would think that is an easy question - do you want to head into Computer Forensics or not?

Quote

what is the most efficient and effective way to study assuming you had forty hours each week over the three month period to prepare?

My thought is obviously to study a college level text book on the topic and then maybe take a week and review a CLEP study guide prior to the actual test.


With zero knowledge about you, your study habits, what you know, or what you don't questions like "the most efficient" is relative up to you. When I studied for the GRE I picked up multiple test prep books, and a book of nothing but practice test. I found my study guide via an amalgamation of those test prep books, and the faux tests helped ID weak spots.


As to your first comment, I honestly don't know much about forensics so I guess I am really asking others consider this to be as interesting an area as traditional programming. Also, are there as many of those types of jobs as opposed to regular programming jobs?

After reading your comment and rereading my post, I agree with you. I guess what I am really trying to ask is a recommendation as to one textbook that covers algebra/trig at a college level, or is the simple answer that all textbooks equivalent?

Thanks for your feedback.
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#4 modi123_1  Icon User is offline

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Re: Mathematics Question ... AND ... Computer Science Masters Question

Posted 10 September 2013 - 10:16 AM

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Also, are there as many of those types of jobs as opposed to regular programming jobs?

Well there won't be as many niche jobs as a general job, right?

What exactly is your expectation from getting a Masters? To have some sort of mega understanding of a whole mess of languages? It sounds like you are treating this like an associates/trades skill route.
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Re: Mathematics Question ... AND ... Computer Science Masters Question

Posted 10 September 2013 - 10:46 AM

View Postmodi123_1, on 10 September 2013 - 10:16 AM, said:

Quote

Also, are there as many of those types of jobs as opposed to regular programming jobs?

Well there won't be as many niche jobs as a general job, right?

What exactly is your expectation from getting a Masters? To have some sort of mega understanding of a whole mess of languages? It sounds like you are treating this like an associates/trades skill route.


I believe you are missing the general tone of the questioning, and that is simply to get additional information from those of you with more experience than I in the respective fields. Yes, I am posing specific questions about the best approach to take towards studying for the CLEP exam, and then following job expectations for each masters track; none-the-less, what I am also asking (implied) is simply for ANY information on the topic(s) as a whole.

I am not asking for a critique in logic.

Your latter question is a very broad assumption based on the questions I posed. As I briefly stated in my original post, I am primarily interested in the masters because I like to learn and am interested in computer science. Secondarily, I am interested in the economic benefit of my decision. As a side note, I already make as much money as I will probably make as a computer scientist, even five years into the profession, so I am actually sacrificing monetarily to do this.

My understanding of an undergraduate computer science degree is that it is formalized training in theory and that programming languages are merely tools unto that end. In fact, one can apply the principles of computer science to any endeavor in life as all of life is "quantifiable" and an "ordering of rules" is worked out though out the totality of our human experience. That last statement may be a bit ethereal in the real world but is indeed the type of inspiration that draws me to this field.

A masters degree in computer science simply goes deeper in the undergraduate core areas, and to some extent explores areas outside of general studies.

A doctoral program is primarily research intensive and is a completely different animal from the master's program.

Of course, anyone reading this post may have already completed all three degrees and will know far more than I what each program truly entails, but I none-the-less offer my perspective.

Again, thank you for your perspective.
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#6 macosxnerd101  Icon User is offline

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Re: Mathematics Question ... AND ... Computer Science Masters Question

Posted 10 September 2013 - 11:29 AM

Precalculus generally covers vectors, polar coordinates, series and sequences, and limits. It's very algebraic. I would pick up a high school precalculus textbook, honestly. You may also want to check out Paul's Notes, under the Algebra section.

As for trig, it's very basic. If you know your right triangle trig and a few identities, there isn't much more to it than that.

Regarding your Calculus, we have a Math resource thread, which links to quite a few of my Calculus tutorials, amongst other things.

Also to note- you'll have to get good at math pretty quickly if you're pursuing a Master's in CS. A lot of the CS theory you will get will require skills comparable to Differential Equations, as well as other topics like Combinatorics, Graph Theory, and Proof Writing.
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Re: Mathematics Question ... AND ... Computer Science Masters Question

Posted 10 September 2013 - 11:47 AM

View Postmacosxnerd101, on 10 September 2013 - 11:29 AM, said:

Precalculus generally covers vectors, polar coordinates, series and sequences, and limits. It's very algebraic. I would pick up a high school precalculus textbook, honestly. You may also want to check out Paul's Notes, under the Algebra section.

As for trig, it's very basic. If you know your right triangle trig and a few identities, there isn't much more to it than that.

Regarding your Calculus, we have a Math resource thread, which links to quite a few of my Calculus tutorials, amongst other things.

Also to note- you'll have to get good at math pretty quickly if you're pursuing a Master's in CS. A lot of the CS theory you will get will require skills comparable to Differential Equations, as well as other topics like Combinatorics, Graph Theory, and Proof Writing.


That is good information. I will work through all of the content you referenced.

As a follow-up: do you think my time horizon and expectation is unrealistic? As said, it has been many years since I have had any math classes but I have had all the way through Calculus I. I am reasonably intelligent and have three months to devote to full time study to get up to speed in precalculus algebra/trig before clepping the courses. If I don't clep the courses, I will be set two semesters back and that is too much time with what I am planning to do.
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#8 macosxnerd101  Icon User is offline

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Re: Mathematics Question ... AND ... Computer Science Masters Question

Posted 10 September 2013 - 11:53 AM

I don't think getting out of the Trig/Precalc work is unreasonable. In terms of your prerequisites, you will want the following at least:
-Two semesters of Data Structures and Algorithms
-Discrete Math or Proofs
-Combinatorics and Graph Theory
-Computer Architecture/Organization/Systems (2 semesters)
-Calc I-II, Diff Eqs, and Linear Algebra

You may find one year to fill all this in less than sufficient.
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Re: Mathematics Question ... AND ... Computer Science Masters Question

Posted 10 September 2013 - 12:06 PM

View Postmacosxnerd101, on 10 September 2013 - 11:53 AM, said:

I don't think getting out of the Trig/Precalc work is unreasonable. In terms of your prerequisites, you will want the following at least:
-Two semesters of Data Structures and Algorithms
-Discrete Math or Proofs
-Combinatorics and Graph Theory
-Computer Architecture/Organization/Systems (2 semesters)
-Calc I-II, Diff Eqs, and Linear Algebra

You may find one year to fill all this in less than sufficient.


Wow! Interesting! My university only requires Cal I/II for the Masters program. I have not looked closely at the course content in graduate school, so it may be that some or all of the additional classes you referred too are taken at that level; but, I suspect that is not entirely the case ...

I wish I had the time and money to spend a solid two years in undergraduate mathematics. :( Of course, I will self-study but obviously I will have plenty to do with the prescribed course work.

Which leads me to this question: to what extent are the various mathematics courses directly related to computer science coursework? Is it more that advanced mathematics trains one how to "think" but not necessarily that knowledge of the various proofs are required to learn/do computer science theory; or, is it in fact that I will be struggling to learn the actual math (on the side) along with learning theory and programming?

Coming all the way back to the working world, it would seem that mathematics is not that big a part of everyday "programming." I speak in generalities, so of course there are exceptions ... but as a general rule.

Although my accounting background did not require as much mathematics as a computer science program, it did require some along with various mathematical calculations within accounting, and finance. ALL of the math and various calculations are automated and I do ZERO of that in the working world. Whereas in school I calculated by hand amortization schedules, depreciation tables, time value of money schedules and probability, in the working world I use software that does every bit of that for me. The learning curve at work is learning how to use the software. The educational background has helped me, in these specific examples, to read the reports generated by the software.

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#10 macosxnerd101  Icon User is offline

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Re: Mathematics Question ... AND ... Computer Science Masters Question

Posted 10 September 2013 - 12:20 PM

In Algorithm Analysis, you will need to solve recurrence relations to find complexity bounds. The methods to do this are the same as in Diff Eqs. Algorithm Analysis will also deal with graph algorithms, so you will want a combinatorics and graph theory background. Your CS Theory classes really deal with proof-writing, and they are really math courses. Linear Algebra is a nice to have, especially if you want to deal with graphics. It also has applications in graph theory, physics, and numerical methods.

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is it in fact that I will be struggling to learn the actual math (on the side) along with learning theory and programming?

This will be the case. It depends on how much theory you get though. As a CS Graduate Student, you should be getting theory, along with your more practical coursework.

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so it may be that some or all of the additional classes you referred too are taken at that level; but, I suspect that is not entirely the case ...

A lot of these prereqs are covered in undergrad CS courses. Honestly, even if you only have one semester of computer organization, you'll probably be fine, unless that's where you find yourself leaning as you get into the curriculum.
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Re: Mathematics Question ... AND ... Computer Science Masters Question

Posted 10 September 2013 - 12:33 PM

Good, straight answers! Thanks!


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so it may be that some or all of the additional classes you referred too are taken at that level; but, I suspect that is not entirely the case ...

A lot of these prereqs are covered in undergrad CS courses. Honestly, even if you only have one semester of computer organization, you'll probably be fine, unless that's where you find yourself leaning as you get into the curriculum.
[/quote]

Sorry to be dumb, but are you saying that probably I am okay with basic math prereqs unless I find that I get interested in graduate cs topics that actually require the more advanced mathematics you have listed?
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#12 macosxnerd101  Icon User is offline

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Re: Mathematics Question ... AND ... Computer Science Masters Question

Posted 10 September 2013 - 12:36 PM

I'm saying you may be okay slightly deficient on your low-level architecture background unless you get into those topics. As a CS grad student, especially one without a strong math and CS background, I would be surprised if you didn't have to get through one CS theory class, which will require a lot of math. For that, you will want Discrete Math and Graph Theory.
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Re: Mathematics Question ... AND ... Computer Science Masters Question

Posted 10 September 2013 - 12:41 PM

View Postmacosxnerd101, on 10 September 2013 - 12:36 PM, said:

I'm saying you may be okay slightly deficient on your low-level architecture background unless you get into those topics. As a CS grad student, especially one without a strong math and CS background, I would be surprised if you didn't have to get through one CS theory class, which will require a lot of math. For that, you will want Discrete Math and Graph Theory.


That is clear. Thanks.

I will have six cs classes and 4 math classes (though cal II) when I enter the program. Three of the undergraduate CS courses will be taken as electives in the graduate program, so following your logic it will indeed probably be less theory and more programming.
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#14 macosxnerd101  Icon User is offline

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Re: Mathematics Question ... AND ... Computer Science Masters Question

Posted 10 September 2013 - 12:46 PM

Hopefully things will pan out well in the end! Good luck!
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