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    #243110 06/18/18 09:23 AM
    Joined: Feb 2010
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    My eldest son, now finishing 10th grade, took calculus at RSM this year and the AP Calculus BC exam at school. He likes programming and intends to major in computer science. What have your children done or considered doing in math after calculus, before college? Are there online courses you recommend? Here are a few that look interesting:

    Harvard EdX Calculus Applied!: Apply tools of single-variable calculus to create and analyze mathematical models used by real practitioners in social, life, and physical sciences.
    (The class applies the concepts of single-variable calculus but does not reteach them. This could give him ideas for a computational science fair project.)

    Imperial College London Coursera Mathematics for Machine Learning Specialization consisting of
    • Mathematics for Machine Learning: Linear Algebra Mathematics for Machine Learning: Linear Algebra
    • Mathematics for Machine Learning: Multivariate Calculus
    • Mathematics for Machine Learning: PCA
    (He is interested in machine learning.)

    AOPS Calculus (Has anyone taken this after a standard calculus course in school? I assume it would cover things in more depth.)

    Stanford Pre-Collegiate University-Level Online Math and Physics has the following math courses:
    • Multivariable Differential Calculus
    • Multivariable Integral Calculus
    • Linear Algebra
    • Modern Algebra
    • Real Analysis
    • Differential Equations
    • Complex Analysis
    • Partial Differential Equations
    • Elementary Theory of Numbers

    Coursera Introduction to Discrete Mathematics for Computer Science Specialization has the following courses:
    • What is a Proof?
    • Combinatorics and Probability
    • Introduction to Graph Theory
    • Number Theory and Cryptography
    • Delivery Problem

    Wesleyan Coursera Introduction to Complex Analysis

    KAIST Coursera Introduction to Ordinary Differential Equations

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    DS, rising sophomore, took AP Calc BC this past year and is hoping to take Linear Algebra and Multivariable Calc at a local college. Unfortunately he will only audit the courses so not get credit but he does not need the credit for high school. He did the AOPS Calc course in spring of eighth and thought it was a good course.

    If this falls through we might look at some of the options you mentioned, thanks!!

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    Thank you for compiling this list - it may be of interest to DS for fun and enrichment similar to the purpose of AoPS. DS took AP Calculus AB in 9th (this past year) and DD will be taking it in 10th so they will need another two courses and one course respectively after AP Calculus BC. Unfortunately, they are required to acquire four math credits in high school and are therefore restricted to credited college/university courses.

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    Yes, thanks for taking the time to post this list.

    DS, up and coming sophomore took honors pre-calc this past year and will take AP Calc BC this next year. We had looked at the Stanford Multivariable Diff Calc for a future course. He has a friend in his junior year who is taking this course this year. He says it moves quick and is very hard so you have to stay up. His comments makes my son say he does not really like this route. He likes a traditional class room.

    On the other hand my son was accelerated in math in the classroom. His friend has taken 2 summer classes to accelerate to this point. Not sure how much that matters.

    The school my son goes to has AP stats and another class Advanced Math Topics. The Advanced math topics is only a last resort based on the quality of the teacher and reports from other kids who have taken the class. It is a weighted course but you will not get any AP/IB exam credit. I am not sure I should let that sway my opinion but I like having the attachment of the AP/IB as some type of measure of the quality.

    AP Computer Science also counts toward math but the same teacher referenced above teaches it too. I base my quality remarks on how many students have gotten 5s on the exams.


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    You say he's thinking CompSci. A few closely related paths could be Computer Engineering or Electrical/Electronics Engineering depending on his interests. He's still young so he has lots of time to explore and figure out which path is the best fit for his interests and/or desired career options.

    The Stanford courses, to me, are more the Engineering side of things. The list is pretty much the list of math courses/topics I covered many moons ago taking Electrical/Computer Engineering. Possible careers - software/firmware/hardware design/verification. All of that calculus and differential equations is required to get into the hardware/analog side of things which IME is not really done in the CompSci path. He could still end up programming if that is what he's interested in.

    More on the CompSci side of things are the ones listed under Coursera Introduction to Discrete... I'm tempted to have to look at the Cryptography course myself - thanks smile I work with it all of the time so I've picked up a few things but I'm curious to know what gaps I have.

    Many companies aren't picky about CompSci vs Engineering and over the years I've even worked with a few Physics and Math majors as well. There are some careers/companies/roles that are more specific though so it would be good to explore options to see what he thinks will be a better fit for him. As one example I don't think I've come across any CompSci working in chip design (even though there are roles where most of it is pretty much programming). On the flip side, I'm guessing there are niches/companies where CompSci is more prevalent but that I never see because of my degree/role.

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    Johns Hopkins CTY offers
    • Linear Algebra
    • Multivariable Calculus
    • Differential Equations
    • Linear Algebra
    • Differential Equations
    • Elementary Number Theory
    • Introduction to Abstract Mathematics
    • Introduction to Complex Analysis
    • Introduction to Real Analysis
    CTY has used the courses of the Stanford-based EPGY for elementary school math classes. Are the classes listed the same as those offered by Stanford listed in the first message?


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