Any good math book reading suggestions?

Just started my freshman year at community college and I’m not taking any math classes this semester so I checked out a couple of math books from the library to read when I can. I’ve started with ” The Golden Ratio: The Story of Phi, the World’s Most Astonishing Number ” by Mario Livio and I’m loving it so far so I’m curious if anyone knows any other math books similar to that relating to calculus or trigonometry. I’m really not at the point where proof after proof can really keep my interest but I do enjoy the background of the discoveries and origins of the methods.

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What exactly is an Ito integral?

When constructing the Ito integral for simple processes, there is a natural intuition in terms of “betting strategies” that can only change at discrete times.

Now when constructing the Ito integral for a general continuous integrand, what we do is approximate the integrand pointwise in L2 by simple processes and then take the L2 limit of the corresponding integrals.

What does this represent? What exactly is an L2 limit of simple integrals? And why L2 in particular?

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[C] What does it take to be a quantitative analyst?

Just a curious teenager trying to get a better understanding of future career options in stats besides from your usual data roles. One thing I heard about a quant career is that it usually requires a graduate degree/PHD and it’s very tough to break in as a recent grad. Any ideas about this? Thanks.

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[E] Worth applying for Master’s this cycle?

Hey all,

I’m a recent grad with a BA in philosophy and am hoping to pursue an MA in stats. However, I’m not sure if I will be able to get in anywhere this admissions cycle.

The good: graduated with a 4.0 from a top 20 school.

The bad: I’ve only taken one calculus course and linear algebra. I’ll be taking a second calculus course this fall.

Do you think any stats programs would grant me conditional admission so long as I complete the necessary math classes by next year? I’d rather not wait another year to apply.

Thanks for your help!

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Math Students: What do you take notes on?

I need some notebooks for the coming school year and I can’t find any online that I really like. I just need them for doing homework and taking notes from books and lectures. I also have pretty small handwriting and I find that most notebooks have lines that are an awkward size.

Any suggestions?

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Finding probability distribution estimates of simulation outputs as functions of simulation parameters

The purpose of this post is to invite discussion on potential solutions to a mathematical problem.

Consider a stochastic simulation for which a set G of parameters determine the dynamics. From a single realization of the simulation, a value Y is measured. Since the simulation is stochastic, Y is a random variable whose probability distribution depends on the parameters G. (Y=Y_G)

The problem: I am interested in finding a parameterized probability distribution estimate of Y, and express the parameters as functions of the simulation parameters in G. So my question is, how could one go about doing this?

What I’m currently thinking of doing is the following procedure:

  • Sample parameter values of G with a grid search
  • For each set G, perform N simulations to obtain an empirical distribution of Y_G
  • Visualize the empirical distributions for some parameter sets G, and choose an appropriate common parametric distribution (e.g. normal, exponential, etc.)
  • For each Y_G, find the MLE’s of the distribution parameters
  • Visualize the MLE parameters M against the simulation parameters G, and try to construct an analytical expression M = f(G) which fits the observations.

There are many scenarios where my proposed approach breaks down. It might be difficult to find a common parametric distribution which can be fit adequately to all empirical distributions of different Y_G. Even if such a distribution is found, it may be difficult to construct the sought after expression f(G).

Please feel free to share experiences with similar problem, or to just brainstorm solution ideas. Thanks.

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[Career] – What are the differences between a “data scientist” and a “data analyst”?

Is there any tangible differences between the two? Does one have more autonomy? Is one more of a PhD level field whereas the other is MS/BS level? Does one involve more computer science than the other? I look up salaries for both and data scientists seemed to make more, but the job descriptions seemed very similar to data analysis. Or are they just industry buzzwords that can mean whatever a particular company wants them to?

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A First Course in Abstract Algebra – Fraleigh

I finished my B. Math a couple years ago and would love some (hopefully free) recommendations on textbooks or online resources to continue my studies. I am not interested in a masters but I would like to continue learning where my thesis left off.

I had several courses in group theory at the 300 and 400 level with another two in ring and field theory at the 500 level. Students at my university could take master level courses with department approval. I loved the book mentioned in the title and ended up doing an analysis on the unsolvability of the quintic for my undergraduate thesis. We touched briefly on galois theory but just enough to prove what we needed.

I am looking for 300 or 400 level resources to continue learning. Any recommendations would be so helpful.

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