Foundational understanding in mathematics for studying honors

[Rhys Sheridan]

Hi all,

I really hope someone can assist me. I have made the decision to gain a more formal qualification in the form of an open university degree in engineering. (MSc Honors) In order to be prepared I would like to brush up on my skills in mathematics (which are almost non exisitent mind you)so as not to waste to much time. Would any body happen to have any advice on what aspect of mathematics I should focus on or even better have any resources they could advise for a beginner. I am fully aware I am being very ambitious by jumping into a degree after 15 years out of any form education but I am passionate, which I hope will offset the pressure. Actually any tips will help me greatly.

Thank you in advance.

 

[IRstuff]

What specific discipline will dictate the amount of math you need. If you already have a BS degree of some sort, then you need to have at least whatever that discipline's math requirements are needed to complete a master's program. Those are usually pretty clearly spelled out in any college catalog.

I have two basic concerns
> cart before the horse -- asking about math requirements without stating desired discipline
> the fact that you seemingly have done no research on your own

Passion is good, but unless you have a specific goal in mind, it's of little use.

TTFN (ta ta for now)
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[Rhys Sheridan]

I dont think you understand my question. I have no degree or formal education of any sort. My degree will be in engineering in general. (there is no focus or specific subject until later on in the course or If I decide to do a masters). I am specifically asking for any advice on what mathematical concepts are best suited to support a general Key conceptual understanding of engineering concepts, that is all, which can be easily inferred from the question.

"Cart before the horse" not really. If you wanted to describe the dynamics of a black hole you would first need to understand gravity.

"Seemingly done no research on my own" I have done lots and in most circumstances it boils down to having an understanding of A level maths. But I wanted to hear it from the horses mouth. To ask someone if I had missed anything, or could give me a perspective based on experience. For example could anyone who has studied engineering in university give me an idea on what concepts they used in their first year.

My goal is to achieve honors in engineering.

 

[SWComposites]

Algebra, Geometry, Calculus .... as a start. What are the stated prerequisites for the degree you are looking at? Not sure what country you are in, but you had better be sure the "open university" is fully and appropriately accredited or you will be wasting time and money.

 

[SlideRuleEra]

Rhys Sheridan - Here are my recommendations:

Start with math that in the USA is per-college, but are the base for higher math used in engineering:

Algebra
Geometry
Trigonometry

Then move to the math common in all branches of engineering:

Differential Calculus
Integral Calculus

A good website to begin with the basics (for free) in all of the above fields is Kahn Academy.

http://www.SlideRuleEra.net

 

[zeusfaber]

One of the strengths of the OU is the foundation modules it offers to bring candidates who haven't followed the usual A Level route up to a common standard. You might have a look at something like this one as a get-you started.

My other half did an OU foundation course in statistics before she launched into her Masters at the Psychology Department of one of the more traditional UK universities and reckons it is one of the best investments she ever made.

A

 

[GregLocock]

To get an idea of what a UK undergraduate engineering course contains try this:

http://teaching.eng.cam.ac.uk/content/part-ia-syllabuses-links-line-resources

Here's the first year

Michaelmas term (24/16L)
The Michaelmas term course concerns revision and extension of concepts which most students will have met at school. It will be given in two versions, a standard course at a pace of three lectures per week and a fast course at a pace of two lectures per week. Both will cover the same syllabus and employ the same example sheets. The fast course is aimed primarily at those who have taken double mathematics at A level and who have good mathematical fluency, the standard course at those with less prior training. Examples papers will include exercises to encourage students to practice mathematical skills learnt in their previous studies.

Vectors (5/3L)
Scalar and vector product.
Moment of a force and angular velocity vectors.
Scalar and vector triple product.
Examples of applications.
Simple vector geometry, vector equations of lines and planes.
Determinant of 3x3 matrices
Functions and Complex Numbers (7/5L)
Definitions and simple properties of the hyperbolic functions.
Statement of Taylor's theorem, examples including trigonometric and hyperbolic function, exp, ln.
Simple ideas of series, approximations, limits, L'Hopital's rule.
Asymptotic behaviour of functions for small and large argument.
Revision of complex arithmetic and representation in the Argand diagram. Idea of a complex function.
De Moivre's theorem, use of exp (iw t)
Introduction to Ordinary Differential Equations (ODE's) (5/3L)
Linear equations of first order, integrating factor, separation of variables.
Second order ODE’s: complementary functions, superposition and particular integrals.
Linear difference equations.
Notions of a partial derivative.
Matrices (7/5L)
Matrices as linear transformations: the range and the null space of a matrix.
The inverse of a 3x3 matrix.
Change from one orthogonal coordinate system to another, the rotation matrix.
Symmetric, antisymmetric and orthogonal matrices.
Eigenvalues and eigenvectors for symmetric matrices.
Special properties of symmetric matrices: orthogonality of eigenvectors, expansion of an arbitrary vector in eigenvectors.
Examples, including small vibrations.
Lent Term (8L)
The course in the Lent and Easter terms introduces ideas which will be new to most students, but which find application across the whole range of engineering science.

Steps, impulses and linear system response (3L)
Introduction to step and impulse functions. Step and impulse response of linear systems represented by ODE's.
Use of convolution to obtain output given a general input.
Fourier series (4L)
Fourier sine and cosine series. Full and half range, consideration of symmetries, convergence and discontinuities.
Complex Fourier series. Physical interpretations, including effect of filtering a general periodic input.
Introduction to probability material in vacation programmed learning text (1L)
Easter vacation - Probability (Programmed learning text, equivalent to four lectures of material)
Notion of probability. Conditional probability.
Permutations and combinations.
Mean,variance and standard deviation of probability distributions.
Discrete and continuous distributions.
The Normal distribution and experimental errors
Easter term (7L)
Functions of Several Variables (4L)
Differentiation of functions of several variables.
Chain rule, implicit differentiation.
Introduction to definition of grad(f).
Stationary values, unconstrained extrema.
Taylor expansion of f(x,y).
Introduction to Laplace transforms (3L)
Basic properties of Laplace transforms.
Laplace transforms as a means of solving ODEs with initial conditions (using tables of transforms for inversion).

You can then click through 2nd year IB third year (IIA) and fourth year IIB in the menu at the top.

So far as I am aware Cambridge's syllabus is pretty much the same as any other for core subjects.

OU is a tough school, good luck.





Cheers

Greg Locock


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[GregLocock]

But assuming it is the equivalent of a 4 or 5 year degree of course that's what you will be learning, so basically you'd need A level maths beforehand,

https://www.cambridgeinternational.org/Images/415060-2020-2022-syllabus.pdf

A lot more stats than I did at A level, and less calculus.


Cheers

Greg Locock


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[CWB1]

Not sure what the standard is on your side of the pond, but stateside most universities expect engineering students to be prepared to begin Calculus their first semester. Some offer a remedial preparatory pre-calc course, others do not, so I would suggest brushing up on algebra and trigonometry in particular.

Best of luck going back btw. I went back at 24 with only a basic trade-school education in the seven years between high school and college. The first semester was a bit unnerving as there was quite a bit to relearn, but after that I definitely had an advantage as I was more serious and better able to focus on my education than most of my younger classmates. I decided early-on to get through it as fast as possible to save money, so after the first semester asked my advisor about going beyond the 18-hour max and as an adult, he trusted me to do so. With lousy scheduling delaying me, I still finished a "four-year" bachelor's in three (almost 2.5) with 160 credits, only 128 being required.

 

[Ron]

@Rhys....how are you going from no university education to MSc? (or maybe I'm missing something in the British terminology) Commendable goal but you have to jump through a lot of hoops to get there.

 

[GregLocock]

CWB1 There's a difference in terminology. In the UK calculus means integration and differentiation. The other stuff gets other names, as shown in the A level syllabus I posted.

Cheers

Greg Locock


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[IRstuff]

I have no degree or formal education of any sort

That's irrelevant; you still need all the math that's spelled in any college course catalog for whatever engineering discipline you select.

"Cart before the horse" not really. If you wanted to describe the dynamics of a black hole you would first need to understand gravity.

My point precisely; you picked black holes to study. If you were going to study operational anplifiers, you wouldn't give hoot about gravity of black holes; that's strictly an astrophysics major thing. Likewise, thermodynamics is not required for EE, but is definitely required for ChemE. You continue to dance around the bush, so the only things that anyone can recommend is the conventional college freshman Calculus and sophomore Linear Algebra, since that's the point where disciplines diverge in math. I took Fourier and Laplace transforms in sophomore year because I was majoring in EE, but MEs, ChemEs, and CS majors didn't.

TTFN (ta ta for now)
I can do absolutely anything. I'm an expert!

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[Rhys Sheridan]

Thank you all very much for the information and advice you have provided. This forum is certainly a good resource to meet some very competent and helpful individuals. Thank you also in advance.

 

[zeusfaber]

@Ron,

The traditional model in English universities (I say English, as the system in Scotland is different) was for a three year BSc(Hons) First Degree. Full-time options - but they very much were options - for advanced study then included a one-year taught Masters, two-year research Masters and (for some people) interminable PhD programme - often taken at a different university from your First Degree

In the early 1980s, some universities started offering four year programmes for promising students where the expectation was that you would come out the end with an MEng but, if you turned out not to be such a promising student after all, you could bail after the third year and still get a Bachelor's degree out of it.

Over the years, that four-year Masters model has more or less turned into the norm - driven largely by the Engineering Council's decision to raise the baseline qualification for Chartered Engineer status from BSc to MSc as part of the SARTOR 3 changes in 1999.

A.

 

[Vibac]

Make sure to check out the YouTube channel 3Blue1Brown. It has fantastic presentations on a lot of medium to advanced math topic. I find it really worthwhile!

 

[Ron]

@zeusfaber....thanks. I thought I didn't quite understand the terminology. Being in the US, I did my undergraduate work under the old system of a 4-1/2 to 5 yr. Bachelor's program in engineering. Under that system, a typical bachelor's degree (say, business or basket weaving) was 180 quarter hours. Minimum for an engineering degree was 202 quarter hours; however, I don't know of anyone who ever completed the program in 202 quarter hours. When I graduated I had 228 quarter hours of credits. Two years later my university switched to a semester system. Still required more hours for engineering than other degrees.