Recent content by Calaver

Thank you to everyone who has replied so far for your thoughts on this topic! I am glad to see that there are indeed possibilities for high school students to contribute in some way to research, even though the opportunities might be difficult to find. I also appreciate those of you who...

Thanks for posting this, as it reminded me that I should still look into interning with a profession, research or otherwise, for the less tangible benefits (e.g. knowing how to dress professionally on a day to day basis). I hadn't even thought of the legal issues that might arise from assisting...

Thank you both for your further replies! Thanks for clarifying your view. That's along the lines of what I expected, but I am glad to see that the students were able to have some positive impact on the lab. Would you say that it is better to wait until the first semester of college to begin...

Thank you to everyone who has replied so far! Do you think that the students gained any valuable skills out of the experience, or was it not a very effective use of their time? Also, did their benefits to the lab group outweigh the costs (i.e. did their "code monkeying" actually help anything...

Quick background: I'm currently a junior (grade 11) in high school who is intending to major in math and/or physics in college. Recently, I had a conversation with a college counselor that turned to my interests in math and physics, including my independent studying of the subjects. The...

The solid dot does not typically indicate continuity at the point (-1,0), rather, it indicates that the function's domain includes the point -1. On the other hand, a circle that is not solid at a point typically indicates that the function either 1) is not defined at that point or 2) has a...

I just recalled another book by Atkins that might serve as an enjoyable preface to Chemical Principles if the person finds that text too difficult. The Periodic Kingdom is a popular science book, which means it does not have exercises or math beyond basic algebra. With that said, I have heard...

I second this recommendation for an introductory chemistry text. I used it last year (self-study/self-improvement) with only the experience of a middle school chemistry course behind me and it was an excellent text. I still use it for reference, and I have been wanting to try to work it all the...

I assisted (minimally) in choosing the textbook for the AP Physics 1 class for my school, and I believe that my recommendation and the one that the teacher decided on was https://www.amazon.com/dp/0321625927/?tag=pfamazon01-20(it could have also been...

I completely agree with what the current consensus is on your summer plans. I urge you to follow bacte2013's advice (especially the part about Atkins over Oxtoby, as Oxtoby is one of the few books I've read so far that I would say was in no way helpful to my understanding of the material)...

I should give a disclaimer before I write anything else: I have not read either of the books (Apostol or Shilov) on analysis but I am currently working through Shilov's Linear Algebra. And since no one else here seems to have read any of Shilov's book (sorry if someone here has that I didn't...

Thanks everyone for your responses so far! I've seen the proof for ℝ before, but didn't recall all of the steps right away. But now I think I've got a proof for 0⋅x=0 (thanks for the hint!). 0⋅x = (0+0)x because of the property that 0 is the identity element of addition. = 0⋅x + 0⋅x because...

Note: I am not in the course where this problem is being offered; it was simply an interesting linear algebra "thought question" that I found online to which I believe I have found a solution. However, there is one step in my solution that I am unsure about, so thank you to anyone who spares the...

Thank you micromass for the second insight this month that meets me where I'm at (the other was the one about advanced mathematics for high school students)! As someone who is currently attempting to self-study linear algebra (albeit very slowly), this post helped me to see what I can expect...

(Bold added by me for emphasis) Where are you going to school that allows you to proceed so quickly to college-level math? :wideeyed: It's not that I don't believe you or that I mean to demean your frustrations, but my experience is not at all similar to yours (I'm currently a sophomore in...