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This felt like it was written by a physicist or engineer. Too much emphasis on differential equations and not enough on things like topology, functional analys

by Py-o7 5y ago

This felt like it was written by a physicist or engineer. Too much emphasis on differential equations and not enough on things like topology, functional analysis and/or non-introductory parts of algebra like say representation theory.

susanrigetti 5y ago
guilty as charged! :)
- bitexploder 5y ago
  As someone with a keen interest in learning Engineering part time, I found your write ups really helpful though! I enjoy learning math but like to have an angle towards a practical and useful application. It keeps me a little more motivated than pure math learning. With ADHD the concept of being able to build cooler things always keeps me going. But somewhere along the way of learning purely theoretical things for too long my brain just loses interest (not enough reward), even though I enjoy it in the moment it is hard to get to the starting line and take the first step after a while :)
mrjangles 5y ago
Yep, I came here to say this. I think it is important that anyone who wants to study math understand that real math is not at all like what you learn in a physics or engineering department. In these departments you will always hear people say things like >"proofs are not useful, all you have to do is memorize the 'trick' they use. Once you know which trick to use, it is easy" or you will hear them say. >"Math isn't about understanding, it is just about learning rules and symbols on paper". This is not mathematics. These things do happen.... in a physics and engineering department. It is, in fact, a descriptions of a physics education, not a description of a mathematics education. For this reason I would be careful taking mathematics advice from physicists too seriously as they may, unintentionally, lead you very far astray.
- susanrigetti 5y ago
  For what it’s worth, the curriculum in this guide is modeled after the math major maps of many universities, including the one I attended (Penn). I would be curious to know what part of an undergraduate math curriculum will lead people very far astray…
  - mrjangles 5y ago
    It's just that it is very much a "mathematics for engineers" style course. I think very few of the subjects outlined there give you a flavor for what "real" mathematics is really all about at all (except for algebra, which you do mention). Apart from the applied stuff you mention, the real core of a mathematics education involves, I think, 4 main areas with significant overlap Group A: number theory, graph theory, combinatorics which shares concepts with Group B: Algebra, Topology, complex analysis, differential geometry, metric spaces...etc which shares concepts with Group C: Functional analysis, measure theory which shares concepts with Group D: probability and statistics. As for the applied math that you mention, you should really need to add vector calculus and I'd highly encourage anyone to take a course on fluid mechanics (from a mathematics department instead of an engineering department) to get a real feel for vector calculus in action.
    - susanrigetti 5y ago
      I suggest taking another look at the list and comparing it to the required courses of the undergraduate math majors at the top 20 universities in the USA. Real analysis, complex analysis, topology, and number theory are there (topology and number theory are both listed as electives since most math programs categorize them as such). Graph theory, functional analysis, differential geometry, probability, and statistics are almost always either electives or graduate courses. It’s funny, because most of the things you mention as “real math” are things that many math undergraduates don’t learn (not until graduate school at least) but that physics students learn as undergraduates (differential geometry, measure theory, functional analysis, etc.).
      - 5y ago
BeetleB 5y ago
> This felt like it was written by a physicist or engineer. I just compared it to my undergrad's math curriculum and it matches up pretty well. Everything you mentioned is an elective.
Jap2-0 5y ago
As someone studying teaching math, I found it interesting to compare her suggestions: - Calc I-IV - Intro to proofs - Linear algebra - (Abstract) algebra I-II - Real analysis - Complex analysis - Ordinary differential equations - Partial differential equations - (Others) to my program plan: - A couple teaching courses (including one for roughly grades 5-8) - Calc I-IV - Statistics (one without calc, one with) - Linear algebra - Discrete - Geometry - Number theory - History of math (apparently not just a history class, I haven't taken it yet) - Abstract algebra and into to topology

by Py-o7 5y ago

susanrigetti 5y ago

guilty as charged! :)

bitexploder 5y ago
As someone with a keen interest in learning Engineering part time, I found your write ups really helpful though! I enjoy learning math but like to have an angle towards a practical and useful application. It keeps me a little more motivated than pure math learning. With ADHD the concept of being able to build cooler things always keeps me going. But somewhere along the way of learning purely theoretical things for too long my brain just loses interest (not enough reward), even though I enjoy it in the moment it is hard to get to the starting line and take the first step after a while :)

mrjangles 5y ago

Yep, I came here to say this. I think it is important that anyone who wants to study math understand that real math is not at all like what you learn in a physics or engineering department. In these departments you will always hear people say things like >"proofs are not useful, all you have to do is memorize the 'trick' they use. Once you know which trick to use, it is easy" or you will hear them say. >"Math isn't about understanding, it is just about learning rules and symbols on paper". This is not mathematics. These things do happen.... in a physics and engineering department. It is, in fact, a descriptions of a physics education, not a description of a mathematics education. For this reason I would be careful taking mathematics advice from physicists too seriously as they may, unintentionally, lead you very far astray.

susanrigetti 5y ago
For what it’s worth, the curriculum in this guide is modeled after the math major maps of many universities, including the one I attended (Penn). I would be curious to know what part of an undergraduate math curriculum will lead people very far astray…
- mrjangles 5y ago
  It's just that it is very much a "mathematics for engineers" style course. I think very few of the subjects outlined there give you a flavor for what "real" mathematics is really all about at all (except for algebra, which you do mention). Apart from the applied stuff you mention, the real core of a mathematics education involves, I think, 4 main areas with significant overlap Group A: number theory, graph theory, combinatorics which shares concepts with Group B: Algebra, Topology, complex analysis, differential geometry, metric spaces...etc which shares concepts with Group C: Functional analysis, measure theory which shares concepts with Group D: probability and statistics. As for the applied math that you mention, you should really need to add vector calculus and I'd highly encourage anyone to take a course on fluid mechanics (from a mathematics department instead of an engineering department) to get a real feel for vector calculus in action.
  - susanrigetti 5y ago
    I suggest taking another look at the list and comparing it to the required courses of the undergraduate math majors at the top 20 universities in the USA. Real analysis, complex analysis, topology, and number theory are there (topology and number theory are both listed as electives since most math programs categorize them as such). Graph theory, functional analysis, differential geometry, probability, and statistics are almost always either electives or graduate courses. It’s funny, because most of the things you mention as “real math” are things that many math undergraduates don’t learn (not until graduate school at least) but that physics students learn as undergraduates (differential geometry, measure theory, functional analysis, etc.).
    - 5y ago

BeetleB 5y ago

> This felt like it was written by a physicist or engineer. I just compared it to my undergrad's math curriculum and it matches up pretty well. Everything you mentioned is an elective.

Jap2-0 5y ago

As someone studying teaching math, I found it interesting to compare her suggestions: - Calc I-IV - Intro to proofs - Linear algebra - (Abstract) algebra I-II - Real analysis - Complex analysis - Ordinary differential equations - Partial differential equations - (Others) to my program plan: - A couple teaching courses (including one for roughly grades 5-8) - Calc I-IV - Statistics (one without calc, one with) - Linear algebra - Discrete - Geometry - Number theory - History of math (apparently not just a history class, I haven't taken it yet) - Abstract algebra and into to topology