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**PatternMan****Member**- Registered: 2014-03-08
- Posts: 194

Bsc, Masters, PhD or anything? I found out I can get 3 years of funding to get a mathematics bsc in the UK So that leaves me around 14 months to go through the A level math syllabus 16-18 and refine my knowledge of the pre A level mathematics. I'll pretty much need to master every topic within those sets because there are two tests called the ABET and Sixth Term Examination Papers (STEP). I will have to take one of them.

""A-level tests mathematical knowledge and technique by asking you to tackle fairly stereotyped problems. STEP asks you to apply the same knowledge and technique to problems that are, ideally, unfamiliar. Here is a quotation from Roger Porkess1 which illustrates why A-level examinations do not test satisfactorily the skills required to tackle university mathematics courses at the highest

levels:

Students following modular syllabuses work much harder and the system rewards them for doing

so. This means that there is a new sort of AC grade student: not necessarily a particularly

intuitive mathematician but someone who has shown the ability to learn the subject successfully

by dint of hard work and, quite possibly, good teaching.!""

In my understanding they mean A level questions only require hard work and a certain amount of intelligence to learn the material. The exams only test your knowledge and your competence of mathematical procedure. Whereas the STEP paper tests competence in mathematical techniques and mathematical intuition.

STEP questions are:

*less routine

*require more dexterity in mathematical manipulation

*The questions may require knowledge from a variety of mathematical areas

I'm not sure I have the ability to do a mathematics degree. If I had my choice I would do a combination of Mathematics and Physics. Mathematics is fun but I only really like useful things. Pure mathematics is done for it's own sake and may be useless. However for some reason we usually find something to apply it to. Physics focuses on the real world. If I studied a combination it would keep my options open to get into science and engineering too right? I would like to do research and/or engineering. So if anyone has done a mathematics and/or a physics degree then please tell me what the experience was like and how the job prospects were.

"School conditions you to reject your own judgement and experiences. The facts are in the textbook. Memorize and follow the rules. What they don't tell you is the people that discovered the facts and wrote the textbooks are people like you and me."

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**ShivamS****Member**- Registered: 2011-02-07
- Posts: 3,640

Hi Patternman;

I do not have a math degree yet, but will attain one in some time. I'll answer some of your questions, but you have a long way to go. Therefore, don't worry too much about these details. If you want to do math, do it. Jobs come and go, but the fun of doing math stays.

Firstly, everyone goes at a different pace, but I don't really see why you would need 14 months to learn algebra and precalclus. Really, learning the techniques would take more like a month. However, learning to apply those to really difficult problems takes much longer. Now, STEP states that they pose non-routine questions. Most exams say that, even the AP Exams and SATs, but then I find that they are full of routine questions. You will probably need a fair bit of problem solving skills, but you are probably safe in assuming that it isn't AMC 12/AIME level. But of course, just because you don't need problem solving doesn't mean that you shouldn't spend time on it. I would recommend that after learning the material (which won't take anything even close to 14 months), you should spent a significant amount of time solving hard problems.

Why don't you have the ability to do a mathematics degree? Are you under the most stupid assumption that to be successful in mathematics and science you need a high IQ, like I did? If so, then throw that thought out of your mind. The only place a high IQ helps is on IQ tests. Now, if your excuse for not doing a maths degree is that you can't solve hard problems like those on contests, it's just as wrong. If it were true, most maths degree pursuers/holders including me would drop out. Problem solving skills are attained, not given to you at birth. The only way to improve on it is to solve very difficult problems. It takes time, but it works. So don't think you don't have the ability. All it takes is hard work and passion.

You don't even know what pure maths is, so how can you not like it? By definition, sure it's developing theory without any application. However, in practice, if it weren't for that theory there would be no physics, engineering etc. Here's a link: http://www.phas.ubc.ca/~mcmillan/rqpdfs/5_qm_in_one_dimension.pdf

As you can see there, maths is the language of those subjects. If it weren't for pure mathematicians, none of those disciplines would have prospered. Also, you can never distinguish between pure and applied maths. Not even between Grothendieck and Erdos. Take a look at both pure and applied, and then decide.

Why can't you do a combination of maths and physics? It's called a double major here in the US. Just keep in mind that physics and engineering are entirely different. There is some overlap, but if you wanted to switch from physics to engineering, you would have to spend at least 2 years in university studying. As for job prospects, you said you wanted to be a researcher, so you really only have one job; that of a researcher.

Anyway, don't stress over this too much now. Learn the maths and sciences and enjoy it. There is a lot of time to decide on your profession.

Nehusthan, I never knew you had a maths degree!

*Last edited by ShivamS (2014-03-28 08:00:39)*

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**eigenguy****Member**- Registered: 2014-03-18
- Posts: 78

I have a BS in Physics and a PhD in Mathematics specializing in Differential Geometry. I started in Physics, which had been my intended direction since 7th grade. But I was always good at math, and once I got through the classes expected for all physics majors, I decided to take the few extra needed to pick up a minor in Math. However, my introduction to real analysis course completely changed my understanding of mathematics. I learned the rigor of true mathematics, and took delight in learning the inner workings of all the things that I had only vague ideas about before. I enjoyed it enough, I took another year and got a double major in Physics and Math instead. Afterwards, an opportunity to get my Masters in Math opened. I followed it and the doctorate after.

Like any PhD program, it was long slog, and I was burned out on the subject by the time I reached the end of it. That, little reputation for my alma mater, and a cyclic glut of new doctorates vs available post-docs (these things go up and down in cycles) meant that I had no success in finding a position after graduating. Instead I spent a few years in manufacturing before an opportunity opened for my present job as a Weight Engineer at an aircraft company (weight engineers track the distribution of weight in the aircraft, which is needed for aerodynamics, stress, loads, and flutter analysis). At first, while a step up from manufacturing, this seemed like a poor fit for my education, but in fact has proven to challenging, enjoyable, and has opened many new avenues of investigation for me.

Like you, I originally considered higher mathematics to be mostly without practical benefit. I have since developed a strong disagreement with that concept. Most of modern technology works by principles that people originally studied as a lark, without believing that it would ever have practical application. Instead, had they not studied it, our lives would be far different, and harder, than they are now. The thing is, you don't know in advance what will prove useful, and what won't. But generally, anything has an application. Hardy used to brag that nothing he did had a practical application (yes, he considered that something to brag about). But since his day, every theory he developed has found practical application.

Whether Physics or Math or Engineering, or some other field is the best fit for you, I don't know. But don't be too quick to choose. When you get to college, look around. See what you find the most intriguing. Then follow it.

"Having thus refreshed ourselves in the oasis of a proof, we now turn again into the desert of definitions." - Bröcker & Jänich

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**PatternMan****Member**- Registered: 2014-03-08
- Posts: 194

I have to think about employment if I don't want to end up doing mathematics in the library and sleeping on park benches in a sleeping bag. A combination of maths and physics would keep my options open. I imagine it wouldn't be difficult to go into finance, programming straight out of that degree. I could do a masters or phd to allow me to go into research or engineering.

I have to learn algebra 2, trigonemetry, some geometry, precalculus and calculus upto, but not including multivariable calculus. A level mathematics has a bit more content than AP. The STEP or ABA are exams set originally by the top universities to test your ability to problem solve to a higher standard using that knowledge.

I would like to contribute to the field in some way and I assume you need a relatively high IQ to do that. I have been doing the AMC 8's and usually solve around 2/3 of the questions on there. I hope I'll get better over time but if I don't master topics it will just make learning new topics harder because they rely on the previous ones I haven't mastered.

Pure math is probably fun but Ideally I want to create new mathematics that is directly applicable to something. I'm no Isaac Newton and don't expect to create a new calculus (not that I wont try xD) so at the very least I would want to do some useful mathematical modelling.

I can do a joint major of mathematics and Physics so long as I can learn the whole of school physics. Actually that would probably be a lot easier after covering calculus.

*Last edited by PatternMan (2014-05-01 12:51:36)*

"School conditions you to reject your own judgement and experiences. The facts are in the textbook. Memorize and follow the rules. What they don't tell you is the people that discovered the facts and wrote the textbooks are people like you and me."

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 92,908

Hi PatternMan;

I slept on lots of park benches, they are a little stiff but you get plenty of fresh air. The good thing is that if you walk through the park you will undoubtedly be mugged. Sleep on the benches and people and muggers will act as if you are not even there.

Oh, I got my degree from Whatsa Matta U. That is why I was on a park bench.

You are a little young to be planning out your entire future. We never really know what tomorrow will bring and besides too much planning makes a person old and ugly. What is important is that you are building a lifelong hobby. You will grow to love it and it will sustain you. In the meantime, have some fun.

**In mathematics, you don't understand things. You just get used to them.**

**I agree with you regarding the satisfaction and importance of actually computing some numbers. I can't tell you how often I see time and money wasted because someone didn't bother to run the numbers.**

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**PatternMan****Member**- Registered: 2014-03-08
- Posts: 194

bobbym wrote:

Hi PatternMan;

I slept on lots of park benches, they are a little stiff but you get plenty of fresh air. The good thing is that if you walk through the park you will undoubtedly be mugged. Sleep on the benches and people and muggers will act as if you are not even there.

You are a little young to be planning out your entire future. We never really know what tomorrow will bring and besides too much planning makes a person old and ugly. What is important is that you are building a lifelong hobby. You will grow to love it and it will sustain you. In the meantime, have some fun.

<-- not as young as you think. 23 is still young but past the age where I have time to discover myself. Luckily I have a general idea of my passions. I admire your Pollyannaism though. I'll just enjoy the subject for the moment.

*Last edited by PatternMan (2014-03-28 11:44:39)*

"School conditions you to reject your own judgement and experiences. The facts are in the textbook. Memorize and follow the rules. What they don't tell you is the people that discovered the facts and wrote the textbooks are people like you and me."

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**PatternMan****Member**- Registered: 2014-03-08
- Posts: 194

eigenguy wrote:

I have a BS in Physics and a PhD in Mathematics specializing in Differential Geometry. I started in Physics, which had been my intended direction since 7th grade. But I was always good at math, and once I got through the classes expected for all physics majors, I decided to take the few extra needed to pick up a minor in Math. However, my introduction to real analysis course completely changed my understanding of mathematics. I learned the rigor of true mathematics, and took delight in learning the inner workings of all the things that I had only vague ideas about before. I enjoyed it enough, I took another year and got a double major in Physics and Math instead. Afterwards, an opportunity to get my Masters in Math opened. I followed it and the doctorate after.

Like any PhD program, it was long slog, and I was burned out on the subject by the time I reached the end of it. That, little reputation for my alma mater, and a cyclic glut of new doctorates vs available post-docs (these things go up and down in cycles) meant that I had no success in finding a position after graduating. Instead I spent a few years in manufacturing before an opportunity opened for my present job as a Weight Engineer at an aircraft company (weight engineers track the distribution of weight in the aircraft, which is needed for aerodynamics, stress, loads, and flutter analysis). At first, while a step up from manufacturing, this seemed like a poor fit for my education, but in fact has proven to challenging, enjoyable, and has opened many new avenues of investigation for me.

Like you, I originally considered higher mathematics to be mostly without practical benefit. I have since developed a strong disagreement with that concept. Most of modern technology works by principles that people originally studied as a lark, without believing that it would ever have practical application. Instead, had they not studied it, our lives would be far different, and harder, than they are now. The thing is, you don't know in advance what will prove useful, and what won't. But generally, anything has an application. Hardy used to brag that nothing he did had a practical application (yes, he considered that something to brag about). But since his day, every theory he developed has found practical application.

Whether Physics or Math or Engineering, or some other field is the best fit for you, I don't know. But don't be too quick to choose. When you get to college, look around. See what you find the most intriguing. Then follow it.

I'll keep that in mind thank you.

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**ShivamS****Member**- Registered: 2011-02-07
- Posts: 3,640

PatternMan wrote:

I have to think about employment if I don't want to end up doing mathematics in the library and sleeping on park benches in a sleeping bag. A combination of maths and physics would keep my options open. I imagine it wouldn't be difficult to go into finance, programming straight out of that degree. I could do a masters or phd to allow me to go into research or engineering.

I have to learn algebra 2, trigonemetry, some geometry, precalculus and calculus upto, but not including multivariable calculus. A level mathematics has a bit more content than AP. The STEP or ABET are exams set originally by the top universities to test your ability to problem solve to a higher standard using that knowledge.

I would like to contribute to the field in some way and I assume you need a relatively high IQ to do that. I have been doing the AMC 8's and usually solve around 2/3 of the questions on there. I hope I'll get better over time but if I don't master topics it will just make learning new topics harder because they rely on the previous ones I haven't mastered.

Pure math is probably fun but Ideally I want to create new mathematics that is directly applicable to something. I'm no Isaac Newton and don't expect to create a new calculus (not that I wont try xD) so at the very least I would want to do some useful mathematical modelling.

I can do a joint major of mathematics and Physics so long as I can learn the whole of school physics. Actually that would probably be a lot easier after covering calculus.

The post I quoted needs to be reported. You need a high IQ to be successful? Have you heard of Feynman, Watson, Alvarez, Shockley? I guess it comes by experience, but I hope you realize what I said in my previous post. I couldn't solve even one AMC 10 problem >#20 on the AMC 10 two-three years ago. Now, I'm topping the Putnam exam. When I started Spivak, I had difficulty solving the first question in the book. Now I'm breezing through the problems in Spivak's Differential Geometry. Why? Do I have a high IQ? No! Is it because I worked hard? Yes! You have a pretty high chance of having an IQ greater then me, so there goes your theory of needing a high IQ for a maths degree. Why are you not Issac Newton? Why was he special? This predetermined inferiority complex is the reason why we don't have Newton's walking around everywhere.

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**PatternMan****Member**- Registered: 2014-03-08
- Posts: 194

ShivamS wrote:

PatternMan wrote:I have to think about employment if I don't want to end up doing mathematics in the library and sleeping on park benches in a sleeping bag. A combination of maths and physics would keep my options open. I imagine it wouldn't be difficult to go into finance, programming straight out of that degree. I could do a masters or phd to allow me to go into research or engineering.

I have to learn algebra 2, trigonemetry, some geometry, precalculus and calculus upto, but not including multivariable calculus. A level mathematics has a bit more content than AP. The STEP or ABET are exams set originally by the top universities to test your ability to problem solve to a higher standard using that knowledge.

I would like to contribute to the field in some way and I assume you need a relatively high IQ to do that. I have been doing the AMC 8's and usually solve around 2/3 of the questions on there. I hope I'll get better over time but if I don't master topics it will just make learning new topics harder because they rely on the previous ones I haven't mastered.

Pure math is probably fun but Ideally I want to create new mathematics that is directly applicable to something. I'm no Isaac Newton and don't expect to create a new calculus (not that I wont try xD) so at the very least I would want to do some useful mathematical modelling.

I can do a joint major of mathematics and Physics so long as I can learn the whole of school physics. Actually that would probably be a lot easier after covering calculus.

The post I quoted needs to be reported. You need a high IQ to be successful? Have you heard of Feynman, Watson, Alvarez, Shockley? I guess it comes by experience, but I hope you realize what I said in my previous post. I couldn't solve even one AMC 10 problem >#20 on the AMC 10 two-three years ago. Now, I'm topping the Putnam exam. When I started Spivak, I had difficulty solving the first question in the book. Now I'm breezing through the problems in Spivak's Differential Geometry. Why? Do I have a high IQ? No! Is it because I worked hard? Yes! You have a pretty high chance of having an IQ greater then me, so there goes your theory of needing a high IQ for a maths degree. Why are you not Issac Newton? Why was he special? This predetermined inferiority complex is the reason why we don't have Newton's walking around everywhere.

Didn't Feynman get a 125 on the IQ test. Though it's not genius it's above average. I don't believe all the success is to do with genes but I think it's a signifcant part of it. I am a critic of the IQ tests for various reasons. I have watched Richard Feynman in lots of videos and he shows great understanding and an ability to put things into laymens terms. He is a nonconventional thinker. I think part of his success was that he didn't make things more complicated than they needed to be.

I'm willing to bet you're smart than you let on. Lots of people don't distinguish talent from skill. As Will Smith said "Skill is developed from hours and hours of working on your craft." A high IQ might help you pick things up quicker but that doesn't mean a person with a lower IQ can't do it too. I actually think someone like me would do better than a lot of people once I acquire those expertise. I just seem to see things differently and make connections other people don't think of. Even though these connections sound ridiculous at first people usually accept them or get emotional over them. So I don't think I have an inferiority complex. It's just I doubt I have a high IQ and was wondering how much that would affect me. Anyway now I have more resolve.

*Last edited by PatternMan (2014-03-28 14:39:17)*

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 92,908

He is a nonconventional thinker.

There is a famous Feynman story that shows that was the reason for his success.

I just seem to see things differently and make connections other people don't think of.

You will succeed but maybe not in the way you are imagining right now.

**In mathematics, you don't understand things. You just get used to them.**

**I agree with you regarding the satisfaction and importance of actually computing some numbers. I can't tell you how often I see time and money wasted because someone didn't bother to run the numbers.**

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**ShivamS****Member**- Registered: 2011-02-07
- Posts: 3,640

PatternMan wrote:

Didn't Feynman get a 125 on the IQ test. Though it's not genius it's above average. I don't believe all the success is to do with genes but I think it's a signifcant part of it. I am a critic of the IQ tests for various reasons. I have watched Richard Feynman in lots of videos and he shows great understanding and an ability to put things into laymens terms. He is a nonconventional thinker. I think part of his success was that he didn't make things more complicated than they needed to be.

I'm willing to bet you're smart than you let on. Lots of people don't distinguish talent from skill. As Will Smith said "Skill is developed from hours and hours of working on your craft." A high IQ might help you pick things up quicker but that doesn't mean a person with a lower IQ can't do it too. I actually think someone like me would do better than a lot of people once I acquire those expertise. I just seem to see things differently and make connections other people don't think of. Even though these connections sound ridiculous at first people usually accept them or get emotional over them. So I don't think I have an inferiority complex. It's just I doubt I have a high IQ and was wondering how much that would affect me. Anyway now I have more resolve. I'm willing to bet you're smart than you let on. Lots of people don't distinguish talent from skill. As Will Smith said "Skill is developed from hours and hours of working on your craft." A high IQ might help you pick things up quicker but that doesn't mean a person with a lower IQ can't do it too. I actually think someone like me would do better than a lot of people once I acquire those expertise. I just seem to see things differently and make connections other people don't think of. Even though these connections sound ridiculous at first people usually accept them or get emotional over them. So I don't think I have an inferiority complex. It's just I doubt I have a high IQ and was wondering how much that would affect me. Anyway now I have more resolve.

Now you are contradicting your self. You say IQ doesn't matter much then the very next sentence you say it does. IQ tests measure things like how well you can distinguish one different thing out of multiple similar things. That has no applications in math. Where are the sites that say that you need to have a high IQ to do a math PhD? I have never read that.

There are three things that are important in order to be a good research mathematician and three things only:

Talent: You must be born with a little bit of talent. I won't deny this. But the type of talent I mean is to make sure your IQ is greater then 90.

Hard work: This is much, much, much more important than talent. You must really prepare to work hard and the breath math every single day. This is where many people fail.

Enjoyment: Enjoy what you do. This is the single most important criteria to decide whether somebody will be successful in math.

IQ is just a number. It is meaningless. It means whatever meaning you give to it. I work with mathematicians everyday, and I can assure you that there are many which do not have a high IQ. I have also met many mathematicians who were quite slow in their thinking process. But it is perseverance which bring them to the top.

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 92,908

Hi;

I do have to say that the people who come in here regularly are way above average intelligence for the US.

**In mathematics, you don't understand things. You just get used to them.**

**I agree with you regarding the satisfaction and importance of actually computing some numbers. I can't tell you how often I see time and money wasted because someone didn't bother to run the numbers.**

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**ShivamS****Member**- Registered: 2011-02-07
- Posts: 3,640

I don't know about others, but certainly not me! I can solve Sudoku or Rubik's Cube that fast like those high IQ people do - which is about the only thing it's useful for.

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**PatternMan****Member**- Registered: 2014-03-08
- Posts: 194

I don't even think intelligence is fixed if by intelligence you mean the ability to absorb and apply knowledge. That's how it's defined in the Oxford dictionary anyway. Technically I have been becoming more intelligent over the past few years then. But it has been used to mean a persons capacity to learn, rememember, reason, problem solve, plan, etc. They must mean natural ability.

I believe a certain amount of this is due to genes since their brains may function faster or be able to focus better or what ever advantage genetics is supposed to give you. For example I'm naturally good at spotting patterns but I don't know why. Sometimes most the details fade into the background and I just see one common pattern over and over. I then get flashbacks of various times I have seen it in my life and the element was common to all of them. It can be maddening. Babies seem to be able to pick up any language in what 3 years? The majority of grown adults can't do that. There are savants that can absorb information in seconds and remember, leading them to learn something in short periods.

The advantage thinkers and adults have imo is that they have a larger knowledge base to pull from. They can also assess and review. To illustrate this you could have a person conventionally considered to be intelligent. He would take Chinese classes and might be able to pick it up faster than me if we used those same methods. But having knowledge of a few other things and sense I can outdo the person considered to be more intelligent.

I could just look up the most common Chinese phrases. I could just learn 1 phrase a day and learn the words in it. Also watch some Chinese media. That is 365 words a year. Even if I only retained 1/3 of that I could probably get by in that country. I would already have some template sentences I could use and just modify a few words in them. Maybe without even trying you would have picked up the grammar because you're using prepackaged grammar structures anyway.

So I think there a lot of factors that contribute to a person getting results.

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 92,908

Hi;

I think the only thing necessary to achieve results is desire. If you keep trying, you will get results.

Winston Churchill wrote:

Success consists of going from failure to failure without loss of enthusiasm.

Check out the blunder I made in that trigonometry thread. Know what I did, I screamed, cried, kicked a few boxes, cursed at some people, held my head in bucket of cold water for 30 seconds and now I am back. Reinvested, and ready to blunder again.

**In mathematics, you don't understand things. You just get used to them.**

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**PatternMan****Member**- Registered: 2014-03-08
- Posts: 194

bobbym wrote:

Hi;

I think the only thing necessary to achieve results is desire. If you keep trying, you will get results.

Winston Churchill wrote:Success consists of going from failure to failure without loss of enthusiasm.

Check out the blunder I made in that trigonometry thread. Know what I did, I screamed, cried, kicked a few boxes, cursed at some people, held my head in bucket of cold water for 30 seconds and now I am back. Reinvested, and ready to blunder again.

xD We're not going to totally agree because I'm a pedantic one. Thank you guys anyway because I just thought of a few good ideas discussing this in this thread and the other one.

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**eigenguy****Member**- Registered: 2014-03-18
- Posts: 78

bobbym wrote:

Check out the blunder I made in that trigonometry thread. Know what I did, I screamed, cried, kicked a few boxes, cursed at some people, held my head in bucket of cold water for 30 seconds and now I am back. Reinvested, and ready to blunder again.

With that remark, I know you are true mathematician!

PatternMan -

IQ tests are a very limited measure of intelligence. True intelligence has many aspects and people tend to be better in some aspects than in others. Yet IQ is a single number. It cannot adequately measure this. That Feynmann got 125 on an intelligence test is a indictment of the test rather than of him. And intelligence itself is not a great predicter of success in any field, even mathematics. I have met mathematicians that I can say with good certainty are less intelligent than I am. Yet they are practicing mathematicians with good accomplishments, whereas beyond my dissertation, I have never accomplished anything in the field.

The question of how far you want to go and in which direction is of course up to you. Don't pursue a degree in anything unless you feel a real desire to do it. But also, don't let ideas about "job availability" steer you away from doing what you love, either. I cannot speak for other professions, but there are good jobs available for those proficient in mathematics, physics, or engineering. Even though my job is engineering, my first boss told me that he preferred to hire those with mathematics or physics backgrounds because engineers generally wanted to do design work, and thus were less likely to stay in weight engineering. Mathematics is applicable everywhere, and those who hire mathematicians for various jobs often find them more valuable than those specifically educated for the job, because we are trained to think logically about issues in general, and therefore spot possibilities that those trained for the job never dreamed of. That was certainly the case for me. (The reasons I couldn't find any job upon graduating had far more to do with me than with a lack of jobs.)

More generally, doctorates in any field can be useful. About a year or two after starting this job, I was sent a survey. Some college student was studying the usefulness of doctorates to business. I don't know what the outcome of that was, but what impressed me was the list of doctorates it was sent to. Though my company has thousands of salaried employees, and I had met only a small number of them, I recognized almost every name on the list. Most of them I knew as being the crucial people in their particular groups. Doctorates were evidently well worth the hire for my company.

"Having thus refreshed ourselves in the oasis of a proof, we now turn again into the desert of definitions." - Bröcker & Jänich

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**PatternMan****Member**- Registered: 2014-03-08
- Posts: 194

eigenguy wrote:

bobbym wrote:With that remark, I know you are true mathematician!

PatternMan -

IQ tests are a very limited measure of intelligence. True intelligence has many aspects and people tend to be better in some aspects than in others. Yet IQ is a single number. It cannot adequately measure this. That Feynmann got 125 on an intelligence test is a indictment of the test rather than of him. And intelligence itself is not a great predicter of success in any field, even mathematics. I have met mathematicians that I can say with good certainty are less intelligent than I am. Yet they are practicing mathematicians with good accomplishments, whereas beyond my dissertation, I have never accomplished anything in the field.

The question of how far you want to go and in which direction is of course up to you. Don't pursue a degree in anything unless you feel a real desire to do it. But also, don't let ideas about "job availability" steer you away from doing what you love, either. I cannot speak for other professions, but there are good jobs available for those proficient in mathematics, physics, or engineering. Even though my job is engineering, my first boss told me that he preferred to hire those with mathematics or physics backgrounds because engineers generally wanted to do design work, and thus were less likely to stay in weight engineering. Mathematics is applicable everywhere, and those who hire mathematicians for various jobs often find them more valuable than those specifically educated for the job, because we are trained to think logically about issues in general, and therefore spot possibilities that those trained for the job never dreamed of. That was certainly the case for me. (The reasons I couldn't find any job upon graduating had far more to do with me than with a lack of jobs.)

More generally, doctorates in any field can be useful. About a year or two after starting this job, I was sent a survey. Some college student was studying the usefulness of doctorates to business. I don't know what the outcome of that was, but what impressed me was the list of doctorates it was sent to. Though my company has thousands of salaried employees, and I had met only a small number of them, I recognized almost every name on the list. Most of them I knew as being the crucial people in their particular groups. Doctorates were evidently well worth the hire for my company.

Yes I'm not sure whether I want to go into research (math or physics), something computer science related, or engineering so a joint math + physics major would probably be best for me. I should just see what I enjoy first. I'll be studying high school maths and physics and depending on how I like it I might do a single rather than joint major.

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**ShivamS****Member**- Registered: 2011-02-07
- Posts: 3,640

caveat: physics, engineering and computer science are very different.

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**PatternMan****Member**- Registered: 2014-03-08
- Posts: 194

ShivamS wrote:

caveat: physics, engineering and computer science are very different.

All require a significant amount of mathematics though.

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 92,908

But it is different types of math, even requires a different mindset.

**In mathematics, you don't understand things. You just get used to them.**

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**ShivamS****Member**- Registered: 2011-02-07
- Posts: 3,640

Math is all of math. For physics, you need calculus, differential equations, real analysis, linear algebra. That's about it.

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 92,908

For physics, you need calculus, differential equations, real analysis, linear algebra. That's about it.

Not if you are deep into Quantum Mechanics. A bunch of them sat around with us and knew more number theory then the all the math gurus we had. Claimed they were working along with Dyson on Riemann's hypothesis!

**In mathematics, you don't understand things. You just get used to them.**

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**ShivamS****Member**- Registered: 2011-02-07
- Posts: 3,640

Well, the QM I am learning right now doesn't use more than that, but of course the mathematical and theoretical physicists need a lot more math. Speaking of, I guess se7en was a fake since Riemann's Hypothesis hasn't been proven yet.

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