Currently an undergrad majoring in CS and stat. Sometimes, I wish I could have double-majored in CS and math instead. But if I did that I would have regretted not majoring in stat. For math, I really like the abstract and axiomatic way of approaching the problem. I think this might be the reason why I did really well in discrete math but did just okay in calculus 3 which was just a plug and chug class (It got so dry and boring that I eventually had to drop it last semester and then took it again this semester which I did pass in the end). I also took a probability course this semester and really enjoyed it. I'm taking an abstract linear algebra class this summer and really excited to learn more abstract/ pure math(Currently self-studying it and enjoying it a lot). For stat, I really enjoy the real-world application and having more tools under my belt that will come in handy in the future (ie. machine learning, data science, etc). The fact that you can interpret real-world data and then even be able to predict/infer is super cool. I feel like Statistics is more of a science than mathematics. It is very misleading to say that statistics is a subset of mathematics. For example, physics, one of the most math-heavy science, is generally perceived as a science even though without a deeper understanding of math, it is impossible to understand physics. The same goes for statistics. Without a deeper understanding of analysis and measure theory, one can only have a surface-level understanding of physics. This is a stage where I am right now. I only vaguely understand Random Variables and only know how to apply them. However, this does not mean statistics is math just the same way that physics is not math. Statistics from what my professor told me is a relatively new field. So there is still a lot of research going on, and sometimes what counts as statistics nowadays can be vague with the rise of data science and machine learning.
stats is literally just a different epistemological approach of mathematics, grounded in what's essentially aggregated probability and order of occurrence/immanence. It's not misleading at all to say stats is a subset of mathematics(imo still wrong, but not misleading), but it is misleading to assume it's a science in itself. In my opinion I would disagree with both statements and claim that statistics is a different way of thinking about math(and i can go in depth, but that would be a lot to type more than ive already yapped).
Actually as a „mathematical statistics” student I can say that although statistics start from the sample and real world setting motivations, the higher the level the more mathematical statistics is. For example time series could be done only studying Hilbert spaces and interpreted as a subfield of functional analysis. Sometimes statistical motivation (or maybe just call it statistics) give rise to a new mathematical objects to study etc.
Great video. I would add that statistics can diverge further into both theoretical and applied stats, wherein the theoretical stats is kind of a hybrid field consisting in one part of being focused on data, sampling, programming, estimation, and machine learning, and the other part focused on probability theory, real/complex analysis, inference, and measure theory. Applied stats tends to feature minimal probability and analysis with a heavier emphasis on programming, ML, and subject specialization (i.e., biostats, spatial stats [GIS], survival analysis/engineering, etc.). As a former undergrad math major completing a masters in stats, I like the combination of being able to practice analysis proofs in one class while coding a program that can output point estimators in another. Heck, I know some statisticians who work ONLY alongside pure math people in the field of number theory analyzing data on the prime numbers. There is a thought that with quantum computing (if/when that becomes viable) we will solve some of the big conjectures in number theory, which could lead to further advancements in engineering and physics. Sorry for the long comment. Cheers.
To clarify, I think the biggest overlap is when one gets to higher stats degrees, and the number of math classes that overlap increases. For instance, in most PhD Statistics programs, you'll have to complete the following math courses: Calc 1 through 3 i.e. single & mv calculus (obviously), 2 semesters of linear algebra making sure you understand how to prove things using operators and isometries, 2 semesters of analysis (usually one real analysis and one on measure theory but sometimes 3 entire semesters of analysis are recommended), and finally 3 math electives, which usually end up being something like a combination of complex analysis, group theory/abstract algebra, or optimization/graph theory courses. The algebra is usually optional and only for those that want to specialize in stats subfields that use it, such as probability theory, time series analysis, or dynamical systems. Those that specialize specifically in statistical programming will also take additional amount of number theory courses (at least 1, maybe 2-3). Not every Stats PhD requires such a high level of math, but most of them do. If anyone wants to go to grad school for statistics, I recommend just doing a B.S. in Mathematics first. If you can double major or major/minor in Statistics and Mathematics, even better. Cheers & thanks again.
As a math lover working on a degree in Data Science, I 100% agree. Stats is often very dependent on how you look at or frame the data. I prefer Calculus for sure.
One way to think about (of course, not perfect!) is that doing mathematics is essentially a deductive process, where we go from the general to the particular. Statistical learning on the other hand is an inductive process, where we attempt to go from the particulars to the general.
I have a course that is called "Mathematical Statistics" that involves a lot of integrals and things like that. Wouldn't that be a type of math course?
I would say so, math and stats have several places where they overlap. Sometimes thinking about statistical objects reveals new mathematical patterns and other times knowing certain mathematical ideas (in this case how to evaluate weird integrals) is a useful tool when approaching statistical problems.
The way I see it, Mathematics is about absolutes, by that I mean absolute Truth. For example, 2+2 = 4 the Proof of that is the impossibility of the contrary. Statistics, in my opinion, does not deal with absolutes, that is why, I know that when my answer is 1 or 0 I am wrong, because statistics does not deal with Truths statements like Mathematics does.
Bro I a freshman in college majored in engineering and switch to health so I have to take calculus in engineering but since I switch I now have to take statistics so which is harder and I am bad at math
Statistics is a science and not a branch of Math. Previously we have added math in computers to solve many issues which are not based on the experiences but now the world is AI and Statistical modesl are going to solve issues which cannot be solved without working on the previous data.
If there’s a 10% chance of failure and you do it 50 times, there’s a 99.5% chance you’ll fail at some point. Does anyone know what the formula is to calculate this?
P fail once = 1 - Prob(never fail) = 1 - .9^50 Since not failing twice would be the probability you succeed (0.9) * (0.9) but instead of twice it’s 50 times. Otherwise just succeed 49 times * fail once =0.1^1 * 0.9^49 All comes down to binomial distribution
@@jonathanhansen4282 Here’s what I’ve been using to find it: Success percentage .9 (90%) raised to the 50th (# of times) = .00515 ( 1/2% ) that it won’t happen = 99.5% chance that it will
Math is a branch of philosophy and statistics is a branch of mathematics. Everything that we do in statistics is mathematically defined and therefore belongs to the realm of mathematics. Give me one example from statistical theory without a mathematical definition then we can talk about math vs statistics. And you are wrong when you say the deeper you study statistics the more math comes into the design. This is the order: basic real analysis ->measure theory -> probability theory -> statistics.
I believe that Statistics is not a branch of Math its kind of a different science. There are two types of problems (1.) Something which can be solved permanently and their will be no further improvements (2.) There is not solution yet but we can improve them (yes its the history which we can review whether its improved or not)
@@Josama0214 I'm not sure what you're referring to with 'interviews,' but sampling techniques, the design of experiments, and census methodologies are all defined through mathematical principles when used in statistics. Statistics is inherently a quantitative field. So, the moment you define a sample space to measure specific outcomes (which is the basic framework of everything you mentioned) you are automatically within the realm of measure theory. If you don't agree, name one sampling technique used by statisticians that is not mathematically defined.
@@Thefare1234 Convenience Sampling, Quota Sampling, Judgemental Sampling, etc. I think you may be confusing Probability with Statistics. Statistics is not pure math at all, any source will tell you that. Just because it uses mathematical concepts doesn't make it a part of math
@@Josama0214 Think about what a statistician would do with any of the sampling techniques you mentioned. Do we use convenience sampling to pick subjects and stare at them without any analysis, or do we measure something about their characteristics and derive conclusions? Regardless of how biased your sample is, there are exactly two things that you can do with your subjects, and both of them are mathematically defined: Either you consider them as your sample space and measure their characteristics, or you consider them as a subset of a sample space, and assume some form of relation between the subset and the sample space. Then you measure their characteristics and make inferences about the population. Therefore, your work only starts when your sample becomes a mathematical object. In other words, in statistics, we only work with mathematical objects, so everything in statistics is required to be mathematically defined. Since there is nothing in statistics that exists outside mathematical principles statistics is necessarily a branch of mathematics.
Ain't stats maths? Why complicate this? Stats has numbers, they have formulas, they have a method to find something. Read somewhere stats is applied mathematics. But stats is considered both art and science and maths is considered science Only that's a only problem maybe.
@@Josama0214 yeah after studying more of it I understood better There is a fundamental difference between two and someone with weak math skills can still be great statistician
Currently an undergrad majoring in CS and stat. Sometimes, I wish I could have double-majored in CS and math instead. But if I did that I would have regretted not majoring in stat.
For math, I really like the abstract and axiomatic way of approaching the problem. I think this might be the reason why I did really well in discrete math but did just okay in calculus 3 which was just a plug and chug class (It got so dry and boring that I eventually had to drop it last semester and then took it again this semester which I did pass in the end). I also took a probability course this semester and really enjoyed it. I'm taking an abstract linear algebra class this summer and really excited to learn more abstract/ pure math(Currently self-studying it and enjoying it a lot).
For stat, I really enjoy the real-world application and having more tools under my belt that will come in handy in the future (ie. machine learning, data science, etc). The fact that you can interpret real-world data and then even be able to predict/infer is super cool.
I feel like Statistics is more of a science than mathematics. It is very misleading to say that statistics is a subset of mathematics. For example, physics, one of the most math-heavy science, is generally perceived as a science even though without a deeper understanding of math, it is impossible to understand physics. The same goes for statistics. Without a deeper understanding of analysis and measure theory, one can only have a surface-level understanding of physics. This is a stage where I am right now. I only vaguely understand Random Variables and only know how to apply them. However, this does not mean statistics is math just the same way that physics is not math. Statistics from what my professor told me is a relatively new field. So there is still a lot of research going on, and sometimes what counts as statistics nowadays can be vague with the rise of data science and machine learning.
stats is literally just a different epistemological approach of mathematics, grounded in what's essentially aggregated probability and order of occurrence/immanence. It's not misleading at all to say stats is a subset of mathematics(imo still wrong, but not misleading), but it is misleading to assume it's a science in itself. In my opinion I would disagree with both statements and claim that statistics is a different way of thinking about math(and i can go in depth, but that would be a lot to type more than ive already yapped).
The teacher friend is VERY happy with this video! And very excited to share with her students!
😁
Actually as a „mathematical statistics” student I can say that although statistics start from the sample and real world setting motivations, the higher the level the more mathematical statistics is. For example time series could be done only studying Hilbert spaces and interpreted as a subfield of functional analysis. Sometimes statistical motivation (or maybe just call it statistics) give rise to a new mathematical objects to study etc.
Great video. I would add that statistics can diverge further into both theoretical and applied stats, wherein the theoretical stats is kind of a hybrid field consisting in one part of being focused on data, sampling, programming, estimation, and machine learning, and the other part focused on probability theory, real/complex analysis, inference, and measure theory. Applied stats tends to feature minimal probability and analysis with a heavier emphasis on programming, ML, and subject specialization (i.e., biostats, spatial stats [GIS], survival analysis/engineering, etc.). As a former undergrad math major completing a masters in stats, I like the combination of being able to practice analysis proofs in one class while coding a program that can output point estimators in another. Heck, I know some statisticians who work ONLY alongside pure math people in the field of number theory analyzing data on the prime numbers. There is a thought that with quantum computing (if/when that becomes viable) we will solve some of the big conjectures in number theory, which could lead to further advancements in engineering and physics. Sorry for the long comment. Cheers.
To clarify, I think the biggest overlap is when one gets to higher stats degrees, and the number of math classes that overlap increases. For instance, in most PhD Statistics programs, you'll have to complete the following math courses: Calc 1 through 3 i.e. single & mv calculus (obviously), 2 semesters of linear algebra making sure you understand how to prove things using operators and isometries, 2 semesters of analysis (usually one real analysis and one on measure theory but sometimes 3 entire semesters of analysis are recommended), and finally 3 math electives, which usually end up being something like a combination of complex analysis, group theory/abstract algebra, or optimization/graph theory courses. The algebra is usually optional and only for those that want to specialize in stats subfields that use it, such as probability theory, time series analysis, or dynamical systems.
Those that specialize specifically in statistical programming will also take additional amount of number theory courses (at least 1, maybe 2-3).
Not every Stats PhD requires such a high level of math, but most of them do. If anyone wants to go to grad school for statistics, I recommend just doing a B.S. in Mathematics first. If you can double major or major/minor in Statistics and Mathematics, even better.
Cheers & thanks again.
There’ some great info here thanks XavierMacX! 🙂
As a math lover working on a degree in Data Science, I 100% agree. Stats is often very dependent on how you look at or frame the data. I prefer Calculus for sure.
calculus and linear algebra would be examples of maths used in stats for general calculations and probability
One way to think about (of course, not perfect!) is that doing mathematics is essentially a deductive process, where we go from the general to the particular. Statistical learning on the other hand is an inductive process, where we attempt to go from the particulars to the general.
I have a course that is called "Mathematical Statistics" that involves a lot of integrals and things like that.
Wouldn't that be a type of math course?
I would say so, math and stats have several places where they overlap. Sometimes thinking about statistical objects reveals new mathematical patterns and other times knowing certain mathematical ideas (in this case how to evaluate weird integrals) is a useful tool when approaching statistical problems.
Appreciate this explanation. Thank you Nathan
The way I see it, Mathematics is about absolutes, by that I mean absolute Truth.
For example, 2+2 = 4 the Proof of that is the impossibility of the contrary.
Statistics, in my opinion, does not deal with absolutes, that is why, I know that when my answer is 1 or 0 I am wrong, because statistics does not deal with Truths statements like Mathematics does.
As an analytics student i can real just wonder how maths and stats have changed the world n will do in upcoming years
great presentation. Keep it up
I’m glad you thought so! Thanks! :D
Bro I a freshman in college majored in engineering and switch to health so I have to take calculus in engineering but since I switch I now have to take statistics so which is harder and I am bad at math
me to
@@mjrachakonda do think statistics is hard intro level?
Cool vid. I’m fucking tripping balls bc idk if my college degree is worth it or not bc it’s not stem
Statistics is a science and not a branch of Math. Previously we have added math in computers to solve many issues which are not based on the experiences but now the world is AI and Statistical modesl are going to solve issues which cannot be solved without working on the previous data.
If there’s a 10% chance of failure and you do it 50 times, there’s a 99.5% chance you’ll fail at some point. Does anyone know what the formula is to calculate this?
P fail once = 1 - Prob(never fail)
= 1 - .9^50
Since not failing twice would be the probability you succeed (0.9) * (0.9) but instead of twice it’s 50 times.
Otherwise just succeed 49 times * fail once
=0.1^1 * 0.9^49
All comes down to binomial distribution
@@jonathanhansen4282 Here’s what I’ve been using to find it: Success percentage .9 (90%) raised to the 50th (# of times) = .00515 ( 1/2% ) that it won’t happen = 99.5% chance that it will
Math is a branch of philosophy and statistics is a branch of mathematics. Everything that we do in statistics is mathematically defined and therefore belongs to the realm of mathematics. Give me one example from statistical theory without a mathematical definition then we can talk about math vs statistics. And you are wrong when you say the deeper you study statistics the more math comes into the design. This is the order: basic real analysis ->measure theory -> probability theory -> statistics.
I believe that Statistics is not a branch of Math its kind of a different science. There are two types of problems (1.) Something which can be solved permanently and their will be no further improvements (2.) There is not solution yet but we can improve them (yes its the history which we can review whether its improved or not)
Sampling Techniques, Interviews, Census, Planning Experiments, etc Are all defined without a Mathematical Definition
@@Josama0214 I'm not sure what you're referring to with 'interviews,' but sampling techniques, the design of experiments, and census methodologies are all defined through mathematical principles when used in statistics. Statistics is inherently a quantitative field. So, the moment you define a sample space to measure specific outcomes (which is the basic framework of everything you mentioned) you are automatically within the realm of measure theory. If you don't agree, name one sampling technique used by statisticians that is not mathematically defined.
@@Thefare1234 Convenience Sampling, Quota Sampling, Judgemental Sampling, etc. I think you may be confusing Probability with Statistics. Statistics is not pure math at all, any source will tell you that. Just because it uses mathematical concepts doesn't make it a part of math
@@Josama0214 Think about what a statistician would do with any of the sampling techniques you mentioned. Do we use convenience sampling to pick subjects and stare at them without any analysis, or do we measure something about their characteristics and derive conclusions? Regardless of how biased your sample is, there are exactly two things that you can do with your subjects, and both of them are mathematically defined: Either you consider them as your sample space and measure their characteristics, or you consider them as a subset of a sample space, and assume some form of relation between the subset and the sample space. Then you measure their characteristics and make inferences about the population. Therefore, your work only starts when your sample becomes a mathematical object. In other words, in statistics, we only work with mathematical objects, so everything in statistics is required to be mathematically defined. Since there is nothing in statistics that exists outside mathematical principles statistics is necessarily a branch of mathematics.
Ain't stats maths?
Why complicate this?
Stats has numbers, they have formulas, they have a method to find something. Read somewhere stats is applied mathematics. But stats is considered both art and science and maths is considered science Only that's a only problem maybe.
No, Calling Statistics math is like calling Physics or computer science math. Just because you use math in a subject doesn't mean that subject is math
@@Josama0214 yeah after studying more of it
I understood better
There is a fundamental difference between two and someone with weak math skills can still be great statistician
Definitely feel like I like stats more than math.
Then it's a great sign that you can do actuarial science well (if you're still haven't reach that stage of choosing a degree)😉
Math is superior. I'm a statistician.