Mathematics vs. Statistics (1 Viewer)

[sida1049]

So my trials start tomorrow with English Advanced paper 1, and for some reason I thought my time would be best spent here instead of going to sleep in preparation for the coming exam.

What is the difference between mathematical thinking and statistical thinking? I'm considering to major in mathematics or statistics (or perhaps even both, but I'm also interesting in an economics major) and I'm wondering is there a significant difference between the way the two areas are approached? The HSC mathematics syllabus poorly deals with statistics (although it seems that's going to change very soon...), so without sampling more of statistics, I have no idea whether I'd enjoy it over a mathematics major (I nearly enjoyed all of the HSC mathematics courses, especially extension 2... although the whole probability and permutations and combinations thing is probably my lowest point).

To those majoring in mathematics, did you enjoy statistics? And to anyone who majored in statistics, why did you choose it over a mathematics major (my initial guess would be applicability)? Any vague contributions on the two areas of study would be greatly appreciated!

 

[Trebla]

So my trials start tomorrow with English Advanced paper 1, and for some reason I thought my time would be best spent here instead of going to sleep in preparation for the coming exam.

What is the difference between mathematical thinking and statistical thinking? I'm considering to major in mathematics or statistics (or perhaps even both, but I'm also interesting in an economics major) and I'm wondering is there a significant difference between the way the two areas are approached? The HSC mathematics syllabus poorly deals with statistics (although it seems that's going to change very soon...), so without sampling more of statistics, I have no idea whether I'd enjoy it over a mathematics major (I nearly enjoyed all of the HSC mathematics courses, especially extension 2... although the whole probability and permutations and combinations thing is probably my lowest point).

To those majoring in mathematics, did you enjoy statistics? And to anyone who majored in statistics, why did you choose it over a mathematics major (my initial guess would be applicability)? Any vague contributions on the two areas of study would be greatly appreciated!

Mathematical thinking kinda assumes certainty, perfect fits and idealism. Statistical thinking assumes uncertainty, imperfect fits and is kinda related to probabilistic thinking.

Taking a simple example, in mathematics you deal with linear equations where all points lie perfectly on the line y = mx + b. In statistics, you deal with linear regression of data where not all points lie perfectly on the line y = mx + b but the line is a 'best fit'.

 

[sida1049]

Mathematical thinking kinda assumes certainty, perfect fits and idealism. Statistical thinking assumes uncertainty, imperfect fits and is kinda related to probabilistic thinking.

Taking a simple example, in mathematics you deal with linear equations where all points lie perfectly on the line y = mx + b. In statistics, you deal with linear regression of data where not all points lie perfectly on the line y = mx + b but the line is a 'best fit'.

Thank you for your reply.

Statistics does sound interesting, albeit I'll have to reassess that later when I actually do statistics.

Did you take many statistics courses as an undergraduate? What did you enjoy about them, and what did you not enjoy? I'm interested in how mathematicians view the area of statistics, as it may provide some kind of insight as to how mathematicians perceive the divide.

 

[mreditor16]

Bump for an interesting topic and discussion.

 

[sida1049]

Bump for an interesting topic and discussion.

Thanks man. Let's try reversing the desolate nature of the BOS mathematics thread.

I vaguely remember reading somewhere that you are undertaking actuarial studies...? How is it? And to keep it at least tangentially on topic, how are the mathematics/statistics components of your degree? And why did you do it? Quite a few of the people in our extension 2 class have expressed their interest for it, but the main reason seems to be either the pay or the job prospects involving the application of mathematics.

 

[mreditor16]

Thanks man. Let's try reversing the desolate nature of the BOS mathematics thread.

I vaguely remember reading somewhere that you are undertaking actuarial studies...? How is it? And to keep it at least tangentially on topic, how are the mathematics/statistics components of your degree? And why did you do it? Quite a few of the people in our extension 2 class have expressed their interest for it, but the main reason seems to be either the pay or the job prospects involving the application of mathematics.

Actuarial studies is quite interesting atm. I'm only a first year student, however, and only have had one lecture of my first actuarial subject. So tbh I can't comment on the nature of the actuarial content, especially whether it is more mathematical or statistical. Hopefully, posters like VBN or nightweaver drop by to give their insights, considering they've done quite a few actuarial subjects already.

As for why I did it, I had strong interests, passion and competence in the areas of commerce (e.g. economics) and mathematics. Considering this and also my interest in the insurance and superannuation industries, the actuarial profession felt like the right fit for me to pursue.

Let me know if you have any other questions

 

[VBN2470]

Put simply, Maths and Stats at uni is much more advanced than high school, it gets increasinly deeper as you progress through your degree (I'm a 2nd year Maths/Stats major). If you really find maths interesting enough, then I'd say go for it, it's much more interesting since it's all about the ideas that are presented to you. You will learn things that you will have never thought to have existed and some of things are quite mind-blowing.

I do Actuarial Studies as well, and that's more applied Maths/Stats in that you learn the basic maths concepts in first year and you apply them to different practical scenarios etc. It's not as mathematically rigourous as a Maths degree, but it still demands a strong mathematical/statistics foundation. For example, in a Maths degree you might have to learn and utilise a wide range of properties of a certain function etc. whereas in Actuarial, whilst it may be beneficial to know these properties in depth, it suffices to know how to apply this function to problems and the rest is just computation.

There are differences between a Maths and Stats major, a Maths major will have you do courses that focus on Pure or Applied Mathematics whilst in Stats some courses will have you learning advanced Probability models and some in statistics i.e. linear regression, hypothesis testing, confidence intervals, modelling etc. Of course, there is an overlap between these various branches of Mathematics, but picking one major will have you focus deeper into that field of study.

What I said is still very broad tbh, there is so much more to it and I can only give you my insight based on my current experiences. It's one of those things you will decide as you progress throughout your degree and gain an exposure to all sorts of things that may or may not interest you.

Personally, I'd say Pure Mathematics is the hardest, it really requires lots of abstract thinking, when you learn one really abstract concept, they build another very abstract one on it and it can get very mind-boggling. All I can say that if you are interested enough and have passion for whatever you want to do, then go for it. Feel free to ask any more questions regarding this subject matter

 

[Trebla]

Thank you for your reply.

Statistics does sound interesting, albeit I'll have to reassess that later when I actually do statistics.

Did you take many statistics courses as an undergraduate? What did you enjoy about them, and what did you not enjoy? I'm interested in how mathematicians view the area of statistics, as it may provide some kind of insight as to how mathematicians perceive the divide.

I more or less majored in Statistics. A lot of the theoretical stuff used in applied contexts interested me the most. A lot of the Statistics concepts are underpinned by probability theory and use a lot of mathematical machinery.

Some people do get turned off Statistics partly because they are uncomfortable thinking in a probabilistic way (other than Statistics being taught badly). In other words, you have to be comfortable thinking in grey not just in black and white.

Using that regression line of best fit example, quite a number of people have difficulty understanding/grasping or are uncomfortable with the idea that a 'data point' is an observed value out of infinitely many possible values; with each value having a specific probability of occurring (this is known as a random variable).

It is much easier and nicer to think of just a single point which is exactly on a line without having to think about the uncertainty or randomness of data being fitted with the line. However, these concepts are necessary when you are trying to fit a model to explain real data.