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Not sure if this is more a difference between UK/US universities as this says it's targeted at "serious undergraduates or graduate students", but we covered all

Not sure if this is more a difference between UK/US universities as this says it's targeted at "serious undergraduates or graduate students", but we covered all of this material in the 1st and 2nd year undergraduate courses at the Universities I've studied at or taught at here.

dataflow 6y ago
It matters what you're majoring in and focusing on. There's only so much time to teach so much material in CS, for example, and there's not much desire from the faculty to teach numerical diff eq solving (and certainly none from most CS students to learn it). The ones that do go to grad school tend to need these more, but they haven't seen them in undergrad so they end up learning what they're lacking in grad school (or late undergrad). That said, do you guys really learn/teach the shooting method, Lagrange interpolation, predictor-corrector methods, QR factorization, etc. as 1st/2nd-year undergrads? For what majors? I feel like this would come at the cost of deferring other topics to later years.
- physicsguy 6y ago
  We don't generally have majors/minors in the UK, so perhaps this is part of it. You do a degree in for e.g. Maths/Physics/Mech Eng, and all of your courses are in that. Yes, we also covered other stuff like splines, finite difference method, too. I think Finite Element was third year where I last taught.
  - dataflow 6y ago
    > You do a degree in for e.g. Maths/Physics/Mech Eng, and all of your courses are in that. "Major" refers to the same things you mentioned (physics, math, EE, etc.), it's not any different in the US. > Yes, we also covered other stuff like splines, finite difference method, too. I think Finite Element was third year where I last taught. Sorry to repeat the question, but again -- in what major (or "for what degree" in your terminology) did you study this? (CS? MechE? Physics? EE?)
    - physicsguy 6y ago
      My background is physics, but most recently was a TA for classes for people in Aero/Mech/Astronautical Engineering (courses were shared between all three programmes) doing this stuff. In that department, beyond the courses covering this stuff which were compulsory, there were additional optional courses for 3rd and 4th year students to do C programming and more advanced numerical methods and stuff like programming paradigms for HPC.
      - dataflow 6y ago
        Yeah, so I think this clears up why. I don't think that "serious undergraduates or graduate students" statement was aimed at physics folks, but at more like CS (and possibly EE) folks. Who would also normally learn (say) programming paradigms, algorithms, data structures, low-level programming like C, etc. in their first 1-2 years, which are topics I'm guessing you wouldn't be covering as physicists. For students in CS (or to some extent EE or more nearby fields) to go in this direction in their first 1-2 years, they'd need to have a very unusual amount of interest in numerical techniques to defer other basic topics to later years (or just overload on technical courses and defer humanities to later).
        dron57 6y ago
        I did EE in Canada and numerical methods were definitely taught in 2nd year of undergrad. Why wouldn't it be?
        dataflow 6y ago
        I said possibly EE, not necessarily. Depends what you mean by "taught" and on what the program itself focuses on. In EE/CS programs you'd be taking half CS courses at least in the beginning, for example. And those EE courses' focuses are often on DSP and digital control rather than (say) simulating analog circuits. If by "taught" you mean "can be taken at that level", then sure, these are such undergrad courses in the US too, and they don't have particularly long prereq chains either, so a 2nd year student could take them if they actually wanted to. But it's not customary, and if by "taught" you mean required as part of the curriculum, it may not be depending on the school. The reasons are varied; again, lack of interest from CS-leaning folks on both sides is one such reason, as is the fact that the world has gone digital and they tend to focus more on linear algebra/DSP/etc. rather than ODEs and PDEs. In general few undergraduate students who aren't forced to take numerical methods in undergrad will do so. And I'm not saying this is a good or a bad thing or trying to justify it, just explaining how it is and what some of their rationales are.
- the_svd_doctor 6y ago
  I learned those (not QR, but ODE methods, basic numerical PDE, non linear equation solving methods, interpolation, etc) in the first semester of my 2nd year of my engineering bachelor. In Belgium.
  - bigger_cheese 6y ago
    Similar story here my Bachelor of Engineering degree in Australia covered Partial Differential Equations, Fourier Transforms, Interpolation, Eigen Vectors etc. The focus was on the mathematics and concepts. We were not taught how to approach these problems using computer code. We were taught very little computer programming in general. When we were taught how to solve problems using computer assistance the focus tended to be on using specific software packages and not on how to write code. I.e. using ANSYS for Fluid Dynamics problems or using Excel's "Solver" for simultaneous linear equations. Edit: QR Factorisation was covered in my first year Linear Alegbra course. For Matrix stuff we used software called "Maple" which was installed in computer lab at university I have never heard of it again since I left uni so I don't think it is all that common. We mostly had to solve problems by hand on paper anyway - which I hated.
    - physicsguy 6y ago
      They did the same sort of things for CFD, but on top of what I described above and in different courses. In the first year course they were using Solidworks Flow but went on to other stuff after that.
- capeterson 6y ago
  I'm about to graduate from a 4 year university in CA (edit: CS major) and we are taught a fairly in depth numerical methods class as part of our 3000 series of classes (i.e. it's intended for third-year students). It's certainly possible to take it in your second year where I am, but usually students opt for other classes that will help them get an internship before they go to numerical methods, so it's a common third year class IMO. It doesn't normally get pushed off farther than that though, since it's a common prerequisite for fourth year classes.
  - physicsguy 6y ago
    We don't really have so many optional choices here early on - in UK Engineering degrees are regulated by the Engineering Council and have to cover set material, or students who graduate from it are not able to register for Chartered Engineer status as quickly (adds an extra 5 years onto the process). For Physics, the courses are generally set to meet requirements set by the Institute of Physics. We do have credits, but it's generally not possible for you to take courses from a higher level - a 2nd year student can't generally take a 3rd year course for e.g. or vice versa. In general, this means that the first two years of all physics/eng degrees in the UK cover almost identical material across all Universities. It's only after that you start to get any choice, and those choices usually relate somewhat to the expertise of the academics at that institution - I did my first degree in a University with very strong condensed matter theory group for e.g. so there were lots of courses on that.
analog31 6y ago
I was a math + physics major. "Numerical analysis" was one of the math courses, but you could also get CS credit for it. We also used numerical methods in our physics courses. The CS curriculum at the university near my house requires two math courses beyond basic calculus, but does not require differential equations. I work at a place that has a mid sized engineering department. The people who regularly handle math related programming tasks tend to have degrees in the physical sciences, and coincidentally are older than 50.
jrumbut 6y ago
I was confused reading the table of contents until I got to the final third which matched what I was hoping to see, and what I think would be of interest to their target audience. My understanding and limited experience is that US universities focus more on software engineering and theoretical computer science, with numerical methods (even very basic ones) left as a later elective/graduate course.
mumblemumble 6y ago
My graduate program was interdisciplinary, and attracted students with a variety of backgrounds, including social sciences, math, and CS. So there was a huge need to have a survey class like this to get everyone to a common baseline level of knowledge. Some knew math but not programming, others knew programming but not math, and still others knew a little programming and a little math, but not quite enough of either.
BeetleB 6y ago
In the US, it is generally expected that incoming students have no exposure to calculus. Of course, many students do study calculus in high school and can sometimes skip these courses in university, but the curriculum assumes they haven't.
- physicsguy 6y ago
  Ah, OK, that's v. different to UK then. Here everyone doing a Physics/Maths/Engineering degree will have A Level Mathematics qualification and a Physics A Level qualification. In the pure Maths part, it covers integration and differentiation (inc. of trigonometric functions, log, exp and by parts), vectors, and 1st order ODEs as a minimum. There is also mechanics though depending on the school you study at, this did not used to be compulsory (you could choose to do Statistics instead). In Physics A Level, it covers general physics topics - using SUVAT equations for e.g., electric circuits, radiation, some very basic QM like photoelectric effect. Knowing calculus is not a requirement for that qualification as it's designed to be independent from Mathematics A Level (at one point you had to take it as well to study Physics, but declinining numbers of students caused them to stop that), but to study most STEM subjects at University you do need both qualifications. Around 50% going on to study for one of these degree courses will go beyond this and will have studied for an A Level in Further Maths. In this you do second order ODEs, complex numbers, matrices, conic sections, and more mechanics. In the Universities I've taught/studied at, the entirety of these Further Maths topics is usually covered in a 1st year + 1st semester course before going on to do harder stuff beyond that. So from that mathematical background, everything numerical methods-like assumes you already have that knowledge almost from the beginning at University.
  - azalemeth 6y ago
    I actually studied things like Newton's method and even Runge-Kutta ODE solution in a numerical methods A-level module (i.e. at school). There are other bits of the curriculum that are quite different too -- like decision maths, which basically was lots of algorithms (routefinding! critical path analysis!). As a result, my university-level courses were very much based on efficient numerical implementations of stable algorithms, and looked a lot at something like how to solve chaotic ODEs, or integrating rather unpleasant functions. (I was actually taught by this person and how to solve his problems! https://mathworld.wolfram.com/Hundred-DollarHundred-DigitChallengeProblems.html https://mathworld.wolfram.com/Hundred-DollarHundred-DigitCha...)

dataflow 6y ago

It matters what you're majoring in and focusing on. There's only so much time to teach so much material in CS, for example, and there's not much desire from the faculty to teach numerical diff eq solving (and certainly none from most CS students to learn it). The ones that do go to grad school tend to need these more, but they haven't seen them in undergrad so they end up learning what they're lacking in grad school (or late undergrad). That said, do you guys really learn/teach the shooting method, Lagrange interpolation, predictor-corrector methods, QR factorization, etc. as 1st/2nd-year undergrads? For what majors? I feel like this would come at the cost of deferring other topics to later years.

physicsguy 6y ago
We don't generally have majors/minors in the UK, so perhaps this is part of it. You do a degree in for e.g. Maths/Physics/Mech Eng, and all of your courses are in that. Yes, we also covered other stuff like splines, finite difference method, too. I think Finite Element was third year where I last taught.
- dataflow 6y ago
  > You do a degree in for e.g. Maths/Physics/Mech Eng, and all of your courses are in that. "Major" refers to the same things you mentioned (physics, math, EE, etc.), it's not any different in the US. > Yes, we also covered other stuff like splines, finite difference method, too. I think Finite Element was third year where I last taught. Sorry to repeat the question, but again -- in what major (or "for what degree" in your terminology) did you study this? (CS? MechE? Physics? EE?)
  - physicsguy 6y ago
    My background is physics, but most recently was a TA for classes for people in Aero/Mech/Astronautical Engineering (courses were shared between all three programmes) doing this stuff. In that department, beyond the courses covering this stuff which were compulsory, there were additional optional courses for 3rd and 4th year students to do C programming and more advanced numerical methods and stuff like programming paradigms for HPC.
    - dataflow 6y ago
      Yeah, so I think this clears up why. I don't think that "serious undergraduates or graduate students" statement was aimed at physics folks, but at more like CS (and possibly EE) folks. Who would also normally learn (say) programming paradigms, algorithms, data structures, low-level programming like C, etc. in their first 1-2 years, which are topics I'm guessing you wouldn't be covering as physicists. For students in CS (or to some extent EE or more nearby fields) to go in this direction in their first 1-2 years, they'd need to have a very unusual amount of interest in numerical techniques to defer other basic topics to later years (or just overload on technical courses and defer humanities to later).
      - dron57 6y ago
        I did EE in Canada and numerical methods were definitely taught in 2nd year of undergrad. Why wouldn't it be?
        dataflow 6y ago
        I said possibly EE, not necessarily. Depends what you mean by "taught" and on what the program itself focuses on. In EE/CS programs you'd be taking half CS courses at least in the beginning, for example. And those EE courses' focuses are often on DSP and digital control rather than (say) simulating analog circuits. If by "taught" you mean "can be taken at that level", then sure, these are such undergrad courses in the US too, and they don't have particularly long prereq chains either, so a 2nd year student could take them if they actually wanted to. But it's not customary, and if by "taught" you mean required as part of the curriculum, it may not be depending on the school. The reasons are varied; again, lack of interest from CS-leaning folks on both sides is one such reason, as is the fact that the world has gone digital and they tend to focus more on linear algebra/DSP/etc. rather than ODEs and PDEs. In general few undergraduate students who aren't forced to take numerical methods in undergrad will do so. And I'm not saying this is a good or a bad thing or trying to justify it, just explaining how it is and what some of their rationales are.
the_svd_doctor 6y ago
I learned those (not QR, but ODE methods, basic numerical PDE, non linear equation solving methods, interpolation, etc) in the first semester of my 2nd year of my engineering bachelor. In Belgium.
- bigger_cheese 6y ago
  Similar story here my Bachelor of Engineering degree in Australia covered Partial Differential Equations, Fourier Transforms, Interpolation, Eigen Vectors etc. The focus was on the mathematics and concepts. We were not taught how to approach these problems using computer code. We were taught very little computer programming in general. When we were taught how to solve problems using computer assistance the focus tended to be on using specific software packages and not on how to write code. I.e. using ANSYS for Fluid Dynamics problems or using Excel's "Solver" for simultaneous linear equations. Edit: QR Factorisation was covered in my first year Linear Alegbra course. For Matrix stuff we used software called "Maple" which was installed in computer lab at university I have never heard of it again since I left uni so I don't think it is all that common. We mostly had to solve problems by hand on paper anyway - which I hated.
  - physicsguy 6y ago
    They did the same sort of things for CFD, but on top of what I described above and in different courses. In the first year course they were using Solidworks Flow but went on to other stuff after that.
capeterson 6y ago
I'm about to graduate from a 4 year university in CA (edit: CS major) and we are taught a fairly in depth numerical methods class as part of our 3000 series of classes (i.e. it's intended for third-year students). It's certainly possible to take it in your second year where I am, but usually students opt for other classes that will help them get an internship before they go to numerical methods, so it's a common third year class IMO. It doesn't normally get pushed off farther than that though, since it's a common prerequisite for fourth year classes.
- physicsguy 6y ago
  We don't really have so many optional choices here early on - in UK Engineering degrees are regulated by the Engineering Council and have to cover set material, or students who graduate from it are not able to register for Chartered Engineer status as quickly (adds an extra 5 years onto the process). For Physics, the courses are generally set to meet requirements set by the Institute of Physics. We do have credits, but it's generally not possible for you to take courses from a higher level - a 2nd year student can't generally take a 3rd year course for e.g. or vice versa. In general, this means that the first two years of all physics/eng degrees in the UK cover almost identical material across all Universities. It's only after that you start to get any choice, and those choices usually relate somewhat to the expertise of the academics at that institution - I did my first degree in a University with very strong condensed matter theory group for e.g. so there were lots of courses on that.

analog31 6y ago

I was a math + physics major. "Numerical analysis" was one of the math courses, but you could also get CS credit for it. We also used numerical methods in our physics courses. The CS curriculum at the university near my house requires two math courses beyond basic calculus, but does not require differential equations. I work at a place that has a mid sized engineering department. The people who regularly handle math related programming tasks tend to have degrees in the physical sciences, and coincidentally are older than 50.

jrumbut 6y ago

I was confused reading the table of contents until I got to the final third which matched what I was hoping to see, and what I think would be of interest to their target audience. My understanding and limited experience is that US universities focus more on software engineering and theoretical computer science, with numerical methods (even very basic ones) left as a later elective/graduate course.

mumblemumble 6y ago

My graduate program was interdisciplinary, and attracted students with a variety of backgrounds, including social sciences, math, and CS. So there was a huge need to have a survey class like this to get everyone to a common baseline level of knowledge. Some knew math but not programming, others knew programming but not math, and still others knew a little programming and a little math, but not quite enough of either.

BeetleB 6y ago

In the US, it is generally expected that incoming students have no exposure to calculus. Of course, many students do study calculus in high school and can sometimes skip these courses in university, but the curriculum assumes they haven't.

physicsguy 6y ago
Ah, OK, that's v. different to UK then. Here everyone doing a Physics/Maths/Engineering degree will have A Level Mathematics qualification and a Physics A Level qualification. In the pure Maths part, it covers integration and differentiation (inc. of trigonometric functions, log, exp and by parts), vectors, and 1st order ODEs as a minimum. There is also mechanics though depending on the school you study at, this did not used to be compulsory (you could choose to do Statistics instead). In Physics A Level, it covers general physics topics - using SUVAT equations for e.g., electric circuits, radiation, some very basic QM like photoelectric effect. Knowing calculus is not a requirement for that qualification as it's designed to be independent from Mathematics A Level (at one point you had to take it as well to study Physics, but declinining numbers of students caused them to stop that), but to study most STEM subjects at University you do need both qualifications. Around 50% going on to study for one of these degree courses will go beyond this and will have studied for an A Level in Further Maths. In this you do second order ODEs, complex numbers, matrices, conic sections, and more mechanics. In the Universities I've taught/studied at, the entirety of these Further Maths topics is usually covered in a 1st year + 1st semester course before going on to do harder stuff beyond that. So from that mathematical background, everything numerical methods-like assumes you already have that knowledge almost from the beginning at University.
- azalemeth 6y ago
  I actually studied things like Newton's method and even Runge-Kutta ODE solution in a numerical methods A-level module (i.e. at school). There are other bits of the curriculum that are quite different too -- like decision maths, which basically was lots of algorithms (routefinding! critical path analysis!). As a result, my university-level courses were very much based on efficient numerical implementations of stable algorithms, and looked a lot at something like how to solve chaotic ODEs, or integrating rather unpleasant functions. (I was actually taught by this person and how to solve his problems! https://mathworld.wolfram.com/Hundred-DollarHundred-DigitChallengeProblems.html https://mathworld.wolfram.com/Hundred-DollarHundred-DigitCha...)