4 ms·

I solve partial differential equations on parallel computers. This is a key competitive advantage for many industrial applications including aerospace, reservoi

I solve partial differential equations on parallel computers. This is a key competitive advantage for many industrial applications including aerospace, reservoir, reactor, and data center design. It is also crucial for medical applications, climate, and many disciplines of computational physics. There are nowhere near enough qualified people in this field. If you are qualified, you can more-or-less have your pick of jobs anywhere in the world. I use every mathematics and physics course I took until part way into my undergraduate studies on a daily basis. In contrast, I believe that I have never had an English course that improved my writing (they emphasized the wrong things for technical writing). Indeed, it would be difficult to find a single thing I learned in any course outside of the hard sciences that has ever added value to my contributions. It is a disservice to people going into fields like biology or social sciences to pretend that mathematics does not play a pivotal role. Many, perhaps most, professional grade tasks in those fields involve designing studies to test a hypothesis or quantify an effect. This requires statistics, and not just an introduction. In the state I grew up in, Fish and Wildlife had one biometrician. He was a coauthor on every paper published by biologists any office in the state because he was needed to design the study appropriately and analyze the results. With one exception: my father has a Masters in biology, but his coursework was primarily in statistics, and he can design his own studies. Just barely, it still takes a significant amount of reading for each study. Math matters.

schmittz 15y ago
On a related note. Much of applied (primarily solid state) physics, materials science, and the engineerings are now designing new materials for use in many applications. Given the vast possibilities, limited funds, and recent development of powerful mathematical models for simulating systems, many companies and research groups have gone to large scale simulations as the primary means for testing new materials systems and only after discovering the possibilities are these constructed for testing. This means a firm grounding in mathematics (and more specifically these techniques: molecular dynamics, density functional theory, etc.) is headed from "crucial" towards "prerequisite" for people to work in these fields.
rfrey 15y ago
Off topic, sorry. Can you elaborate on what "this field" is? Do you mean deep maths training in PDEs, or is a specialty within computing you mean?
- jedbrown 15y ago
  Broadly speaking, the field is Computational Science and Engineering (CS&E). It occupies the space between applied mathematics, engineering, physics, and software (high and low level). CS&E picks up around where physicists write the equations they would like to solve and handles aspects like discretization, solvers, optimization, and uncertainty quantification. Software is needed for each of these steps, and it usually needs to be high performance, scale on diverse parallel architectures, and be extensible to accommodate new problems. Something that I find especially interesting is adjusting the discretization so that it is better suited to the hardware that is available (e.g. reducing memory bandwidth requirements in exchange for more flops which are relatively cheaper) while maintaining scalability and robustness. Looking at the plenary talks [1] for the upcoming ICIAM meeting might provide some perspective on the field (perhaps slightly biased towards applied mathematics). Part of the difficulty in finding qualified people is that there are few universities with courses aimed at the core of CS&E. Instead, each discipline teaches a subset as viewed from their own corner. The whole is definitely greater than the sum of the parts. The status quo curriculum is a recognized problem that will hopefully be resolved in the next few years. [1] http://www.iciam2011.com/index.php?option=com_content&view=article&id=12&Itemid=26 http://www.iciam2011.com/index.php?option=com_content&vi...
  - Plimsoll 15y ago
    You got me interested. I'm personally studying theoretical physics and have studied all computational courses they give at my university. Seeing these computational tasks from other angle would certainly be pleasant experience. Can you recommend any comprehensive book about CS&E or link to some university's course listing (assuming such list has recommended readings for those courses)
    - jedbrown 15y ago
kd0amg 15y ago
I use every mathematics and physics course I took until part way into my undergraduate studies on a daily basis. I think this highlights an issue I have with the meme that with a major in math, you can do anything. What you can do with a math degree still depends on what you learn aside from pure math (essentially domain knowledge), be it in elective coursework or on your own. "You can be a physicist"? Yes, I could if I'd studied physics more. I would strongly advise other math majors to take a minor or a second major (my other major was CS, where the math background definitely helps, and it would be nice to have even more).
- mturmon 15y ago
  This is an insightful comment. My first-order take had been that the lucrative jobs that the video advertises are plentiful only if the "math person" is also proficient at some type of computing. Reason is, I've known a lot of mathematically talented people who are not able to compete for these kind of jobs because they have no sense of how to compute with their abstractions. But I think your idea captures the problem with the video better than the simplistic "lack of computing expertise" does. The budding "math person" that the video targets could do quite well at, say, a biological or finance application, even without being computer-savvy, just by acquiring expertise in these areas.

schmittz 15y ago

On a related note. Much of applied (primarily solid state) physics, materials science, and the engineerings are now designing new materials for use in many applications. Given the vast possibilities, limited funds, and recent development of powerful mathematical models for simulating systems, many companies and research groups have gone to large scale simulations as the primary means for testing new materials systems and only after discovering the possibilities are these constructed for testing. This means a firm grounding in mathematics (and more specifically these techniques: molecular dynamics, density functional theory, etc.) is headed from "crucial" towards "prerequisite" for people to work in these fields.

rfrey 15y ago

Off topic, sorry. Can you elaborate on what "this field" is? Do you mean deep maths training in PDEs, or is a specialty within computing you mean?

jedbrown 15y ago
Broadly speaking, the field is Computational Science and Engineering (CS&E). It occupies the space between applied mathematics, engineering, physics, and software (high and low level). CS&E picks up around where physicists write the equations they would like to solve and handles aspects like discretization, solvers, optimization, and uncertainty quantification. Software is needed for each of these steps, and it usually needs to be high performance, scale on diverse parallel architectures, and be extensible to accommodate new problems. Something that I find especially interesting is adjusting the discretization so that it is better suited to the hardware that is available (e.g. reducing memory bandwidth requirements in exchange for more flops which are relatively cheaper) while maintaining scalability and robustness. Looking at the plenary talks [1] for the upcoming ICIAM meeting might provide some perspective on the field (perhaps slightly biased towards applied mathematics). Part of the difficulty in finding qualified people is that there are few universities with courses aimed at the core of CS&E. Instead, each discipline teaches a subset as viewed from their own corner. The whole is definitely greater than the sum of the parts. The status quo curriculum is a recognized problem that will hopefully be resolved in the next few years. [1] http://www.iciam2011.com/index.php?option=com_content&view=article&id=12&Itemid=26 http://www.iciam2011.com/index.php?option=com_content&vi...
- Plimsoll 15y ago
  You got me interested. I'm personally studying theoretical physics and have studied all computational courses they give at my university. Seeing these computational tasks from other angle would certainly be pleasant experience. Can you recommend any comprehensive book about CS&E or link to some university's course listing (assuming such list has recommended readings for those courses)
  - jedbrown 15y ago

kd0amg 15y ago

I use every mathematics and physics course I took until part way into my undergraduate studies on a daily basis. I think this highlights an issue I have with the meme that with a major in math, you can do anything. What you can do with a math degree still depends on what you learn aside from pure math (essentially domain knowledge), be it in elective coursework or on your own. "You can be a physicist"? Yes, I could if I'd studied physics more. I would strongly advise other math majors to take a minor or a second major (my other major was CS, where the math background definitely helps, and it would be nice to have even more).

mturmon 15y ago
This is an insightful comment. My first-order take had been that the lucrative jobs that the video advertises are plentiful only if the "math person" is also proficient at some type of computing. Reason is, I've known a lot of mathematically talented people who are not able to compete for these kind of jobs because they have no sense of how to compute with their abstractions. But I think your idea captures the problem with the video better than the simplistic "lack of computing expertise" does. The budding "math person" that the video targets could do quite well at, say, a biological or finance application, even without being computer-savvy, just by acquiring expertise in these areas.