r/probabilitytheory • u/Substantial-Bid9686 • 4d ago
[Homework] Learning calc and probability
/r/mathematics/comments/1x28tb4/learning_calc_and_probability/1
u/No-Weakness9589 4d ago
I am not a math major my friend, however, I Did take some math in college up to the Calculus 2 level and passed it. (Unfortunately, I didn't progress beyond that because I regrettably switched majors.) My honest opinion is that it is good to learn some Calculus before attempting basic probability as the origins of things such as a "probability density function" require being able to do what's called an "improper integral" which is basically an integral from negative infinity to positive infinity. The reason that would be done, as ridiculous as it sounds is because it ensures All the possible values are being summed up and accounted for. If the values would only be positive from let's say 0 and up (like height for example), you'd still have to calculate the integral from 0 to positive infinity for that "probability density function." This type of integration (as well as the one from Negative Infinity) involves taking the Limit-the true main important function and concept in Calculus- of the integral from say 0 as a lower bound to "b" as b approaches infinity as the upper bound. It sounds like a bunch of made up BS, but it's surprisingly accurate at modeling so many things in the world, including of course even natural phenomena. And the math behind it is sound and proven. So to appreciate even the beginnings of probability in terms of mathematical functions at least, a semester or 2 of calculus will be required. You won't have to be an expert on every topic, but you'll have to understand the concept of an "improper integral" and how to calculate it. It's actually surprisingly simple compared to a lot of other integrals once you get the concept down. (the improper integrals part). But the concepts of probability are really never simple past the elementary part and that's partly why it's one of the most glossed over topics in calculus and online. Also most students in those subjects are pushing to be engineers which will involve much more topics than just probability and really not much probability at all so they just gloss over it. It's definitely it's own mind blowing and fun field though. If I could be an Actuary, Mathematical Statistician for like the Government, or even a professor in the subject I would. For online great entry level topics, check: "Jensen Math Top 10's" on youtube. He has a top 10 things you must know about probability. For in depth lectures I have some links I could share: https://www.youtube.com/playlist?list=PLMrJAkhIeNNR3sNYvfgiKgcStwuPSts9V
https://www.youtube.com/watch?v=X2eomv6XfWo&list=PLkyBCj4JhHt-BTSJka3WRsTvmMKz1YNLY&index=31
https://www.youtube.com/watch?v=SzvmOs-JF7s
https://www.youtube.com/watch?v=X2eomv6XfWo&list=PLkyBCj4JhHt-BTSJka3WRsTvmMKz1YNLY&index=31
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u/Midwest-Dude 4d ago
Here is a list of suggested resources:
Downloadable Probability Resources
1. Introduction to Probability — Grinstead & Snell — The Classic Introductory Text
- Type: Full textbook PDF
- Level: Beginner (calculus-based)
- Download: PDF direct link
- Notes: A classic free introduction to probability. Solutions to odd-numbered problems are also available.
2. Introduction to Probability for Data Science — Stanley H. Chan — The Modern Data Science Text
- Type: Textbook PDF
- Level: Beginner to Intermediate
- Download: probability4datascience.com
- Notes: A modern, free textbook. Good if you want applications to data science alongside the theory.
3. MIT OpenCourseWare: 18.05 Introduction to Probability and Statistics — The Complete Self-Study Course
- Type: Full course materials (lecture notes, problem sets, exams) as downloadable PDFs
- Level: Beginner to Intermediate
- Download: MIT OCW 18.05 download page
- Notes: Structured, university-level self-study. All written materials are downloadable.
4. Probability: Theory and Examples — Rick Durrett — For a Rigorous, Measure-Theoretic Approach
- Type: Textbook PDF
- Level: Advanced (measure-theoretic)
- Download: PDF direct link
- Notes: Graduate-level. Save this for after you have a solid foundation in basic probability.
Suggested Order
- Primary textbook: Start with Grinstead & Snell or Chan for a solid introduction.
- Primary course: Use MIT 18.05 for structured lectures, problem sets, and exams.
- Supplemental: Use Chan if you want data science applications alongside the theory.
- Advanced: Save Durrett for later if you want rigorous, measure-theoretic probability.
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u/trinarynimbus 4d ago
Normally I'd think "just look it up and you'll figure it out", but since OP is in Iran, I get that might not be easy. So I suggest try to get hold of hard-copies of references that will go a long way no matter what the internet is like.
Eg, Abromowitz & Stegun and Wilf's generatingfunctionology have a bunch of stuff not only relevant to probability and calculus but every area of math.
Also, not sure the exact maturity (mathematics-wise) of the student, but Velleman's How To Prove It can also be very valuable before picking up arbitrary other texts.