Approaching My 10 Week "Summer" Study Plan

[StudentOfScience]

If you want to read the pdf version of the document, it is attached to this post.

Warning! You can say that this is a long post.

Note that the questions can be found in the sections themselves or in appendix A
Introduction
I had planned to spend about the whole summer - about 10 weeks - studying in order to cover various subjects in the experimental sciences. I, unfortunately, wasted much of the summer. Now, I am left with about five and a half weeks at most to go through the crucial chunk of the material. This means that I’ll have to cover the material during school as well. As a little background, I am in high school looking to go above the AP level in the sciences (granted, those courses are challenging, but I still want to go even farther[1]). The subjects that I wish to cover include the following:

· Classical Mechanics

· Classical Electrodynamics

· Real Analysis (in both one and multiple variables)

· Complex Analysis

· Linear Algebra

· Ordinary Differential Equations

· Partial Differential Equations

· Molecular and Cell Biology

· Anatomy

· Physiology

· General Chemistry (using Oxtoby)

· Organic Chemistry

· Multivariable Calculus (for electrodynamics)

This is definitely a daunting task (and I am probably being “in over my head”)! I have background in single variable calculus and introductory biology, if that helps. My “plan” was to cover the subjects that were scheduled for the upcoming school year so that I could skip those classes and take more advanced classes. Those classes are mechanics, probably electrodynamics, anatomy, physiology, and general chemistry.

At this point, all I’ve given you is information; this is a forum, so I’ll ask some questions! I’m not sure if I do use five weeks to cover mechanics, electrodynamics (and enough multivariable), anatomy, physiology, and general chemistry that I’ll have enough time to cover the remaining subjects - real and complex analysis, ordinary and partial differential equations, linear algebra, and organic chemistry. For more information as to what level I want to cover these courses, see the “Textbook” section.

The “Techniques” section includes study techniques that I may plan to use in order to go through this material. The “Time Management and Allotment” section includes possible propositions on how I can cover the material in a timely manner.

Techniques
Mathematics and Physics
I’ll just give a basic rundown; the details can be found from this thorough answer by Mark Eichenlaub on Quora (I’m not asking you to go through it all; it’s informative but long). From the answer, I quote:

Taken together, this yields enough practical advice to chew on for months or years. To summarize, when you are learning something new:

· Try to figure it out for yourself

· If you get stuck, take a peek at your textbook to get the main idea

· Teach the idea to someone else

· Once you've learned something, repeat the entire reasoning behind it for yourself, working through each detail

· Ask yourself Pólya's questions when you're stuck

· Use Young and Newport's techniques to map out the ideas of your class and relate them to your prior knowledge

· Make Anki decks and review them a few minutes a day to retain what you've learned

· Make sure your study sessions include all the principles of deliberate practice, especially feedback, challenge, and attention

· Build an image of yourself as someone motivated by learning and proud of having worked hard and effectively rather than as someone proud of being smart or renowned.

· Find a organizational system that let's you handle all the details of life smoothly and efficiently.

· Search for the flow state, notice when you enter it, and put yourself in position to find flow more and more often.

· Work on different subjects, reviewing both advanced and basic material. They will eventually all form together in your mind, and you're likely to have to take at least two passes at any subject before you understand it well.

· Take care of your physical health.

Basically, it’s about the “struggle”. Therefore, for physics and mathematics, I could try to prove every theorem/derivation that I can get my hands on to. Furthermore, I should try the challenging questions (and inevitably go to PF when I’m stuck after giving an honest effort). Occasional review in the form of “how was this question answered or proven” would be helpful. My concern is how to do this method in an efficient way, since it seems like this would take a long time. Other than that, this method appears to be foolproof as long as I put in the effort.

Biology and Qualitative Chemistry
The previous section mentioned Anki decks, which I expect to be immensely useful for anatomy (I suspect that anatomy could be mastered with a lot of practice and memorization). However, I’m not sure if approaching molecular and cell biology, general chemistry, organic chemistry, and physiology in the same way would be effective. Could I have some advice? Keep in mind that I am very detail-oriented but still want to see the big picture. A fast and effective note-taking method (or using the Anki decks) may be desired. However, you all know more, so I would like to hear what you have to say.

Textbooks
· Mechanics

o Morin

o Goldstein (after Morin, if there is time)

· Electrodynamics

o Griffiths (and possibly some of the problems in Purcell)

o Jackson (after Griffiths, if there is time)

· Anatomy

o Gray’s Anatomy (41st edition)

· Physiology

o Guyton

· General Chemistry

o Oxtoby

· Organic Chemistry

o Clayden

o Advanced Organic Chemistry: Part A and Part B (Carrey), if there is time after Clayden; or, alternatively, March if there is time after Clayden

· Molecular and Cell Biology

o Alberts

o Watson

· Complex Analysis

o Ahlfors

o Conway (vol. 1 and vol. 2), possibly

o Narasinham (only if I’m feeling very ambitious and have enough time as well as meeting the prerequisites)

· Real Analysis

o I’m not sure; I’d like some recommendations. I’ve considered Rudin, Zorich (vol. 1 and vol. 2), Thompson - Bruckner, Loomis/Sternberg (for multiple variables)

o Other suggestions would be appreciated

· Ordinary Differential Equations

o I’m in a similar situation here as with real analysis; which book(s) should I use? I’ve considered Hirsch/Smale (if I use this, it would be desirable to use editions 1 and 2), Ross, Miess, Perko, Coddington (the Theoretical one), possibly Arnol’d

· Partial Differential Equations

o I’ve considered using Strauss for this one

· Linear Algebra

o Kenneth - Hoffman

o I may use another book such as Strang just so I can also do “mechanical” problems so that I am not just left with the theory

§ Note: this is not to say that Strang’s “Linear Algebra and It’s Applications” is easy or that it is not theoretical

Time Management and Allotment
By now, you can probably tell that there is an immensive amount of material that I want to go through. In fact, I’ve calculated that I would have to cover about 15,500 pages of science/math in about 10 weeks. Of course, page count is not the most important factor; one page of challenging problems would most likely take longer than a page of text with diagrams. Nonetheless, numerically, this means I must average about 3 minutes to read a page if I spend 12 hours a day studying. This is extremely fast, especially since I am concerned about the detail. Even if I spend 15 hours a day studying, this leaves me with 4 minutes to complete a page, which is better, but it is still a stretch. This still is not possible though for the challenging problems. Is there a magic number of how long a problem should take before I give in (note that I don’t readily give up on some problems)? If I spend between 12-15 hours a day studying, is it possible to cover all of this material in 10 weeks? What will I have to do to be able to study faster, yet being able to know, understand, and retain the information at a deep level? How much time should I spend on each subject (i.e. how many hours of the 12-15 should I allot to, say, mechanics)?

Appendix A: List of Questions from OP (Original Poster)
1) I’m not sure if I do use five weeks to cover mechanics, electrodynamics (and enough multivariable), anatomy, physiology, and general chemistry that I’ll have enough time to cover the remaining subjects - real and complex analysis, ordinary and partial differential equations, linear algebra, and organic chemistry. For more information as to what level I want to cover these courses, see the “Textbook” section. (see “Introduction”)

2) My concern is how to do this method in an efficient way, since it seems like this would take a long time. (see “Mathematics and Physics” under “Techniques”)

3) However, I’m not sure if approaching molecular and cell biology, general chemistry, organic chemistry, and physiology in the same way would be effective. Could I have some advice? Keep in mind that I am very detail-oriented but still want to see the big picture. A fast and effective note-taking method (or using the Anki decks) may be desired. However, you all know more, so I would like to hear what you have to say. (see “Biology and Qualitative Chemistry” under “Techniques”)

4) Real Analysis (book recommendations)

a. I’m not sure… I’d like some recommendations. I’ve considered Rudin, Zorich (vol. 1 and vol. 2), Thompson - Bruckner, Loomis/Sternberg (for multiple variables)

b. Other suggestions would be appreciated

5) Ordinary Differential Equations (book recommendations)

a. I’m in a similar situation here as with real analysis; which book(s) should I use? I’ve considered Hirsch/Smale (if I use this, it would be desirable to use editions 1 and 2), Ross, Miess, Perko, Coddington (the Theoretical one), possibly Arnol’d

6) Is there a magic number of how long a problem should take before I give in (note that I don’t readily give up on some problems)? If I spend between 12-15 hours a day studying, is it possible to cover all of this material in 10 weeks? What will I have to do to be able to study faster, yet being able to know, understand, and retain the information at a deep level? How much time should I spend on each subject (i.e. how many hours of the 12-15 should I allot to, say, mechanics)?
Thank you all so much for taking the time to read this long post. I appreciate your help and your tolerance to my obnoxious questions. I don’t know if I will follow through with this plan, but I hope that I really do go through with it.[1] I haven’t taken AP Chemistry or AP Physics C at the time of writing this

 

[micromass]

This is insane.

 

[Mondayman]

I applaud your ambition, but you'll have to be a bit more realistic about what you can and cannot accomplish in ten weeks. Most university level courses cannot make it through the entirety of those textbooks over a full semester, let alone in ten weeks. It would also make more sense to study for AP classes using AP level textbooks or other sources.

Also, while I understand the desire to get ahead during the summer, bear in mind that studying that much everyday is extremely draining. The last thing you want is to start the school year already burnt out!

 

[MarneMath]

Speaking that a person can literally spend an entire week on 5 pages in Rubin. I doubt you would be able to cover a self-study Real Analysis project in 10 weeks alone, much less coupled with anything else on that list. There'a HUGE DIFFERENCE between reading something and understanding something. I typically advise students towards the latter.

 

[Dishsoap]

If you spend the next 5 weeks (24/7) reading, you could read all of the books on that list.

You would not understand them. But you could read them. Is that what you're going for? If not, it is impossible. Not too ambitious, just simply impossible, full stop.

 

[micromass]

If you spend the next 5 weeks (24/7) reading, you could read all of the books on that list.

I doubt even that actually...

 

[amys299]

Why are you even doing this? This is the most ineffective way to spend your time, especially if your aim is a understanding of the subject.

 

[bacte2013]

Is this a joke? What is your goal? Is your goal self-enrichment with learning or preparation for some competitions (Science Olympiad, Chemistry Olympiad, etc.)? Some of textbook you mentioned are used widely for competitions (Oxtoby, Alberts). If you aim for self-enrichment with strong curiosity to the mathematics and science, I can offer you some good starting plans. I am an undergraduate majoring in mathematics and microbiology, so my advice might not be insightful as others like Professor micromass.

For mathematics, focus on the introductory analysis and linear algebra. You can learn other topics you mentioned well if you properly learned those two fields I mentioned. For analysis, get Pugh's Real Mathematical Analysis along with Tao's Analysis I-II or Goldberg's Methods of Analysis. Those books are much better than Rudin for first introduction. For linear algebra, get Hubbard/Hubbard book; it covers vector calculus and linear algebra very well (good balance in applications and theories). You might want to also check out APEX Calculus III for multivariable calculus and Korner's Vectors: Pure and Applied for linear algebra. I personally like Hoffman/Kunze, but you need background knowledge in algebra to get most out of that book.

For biology, I assume you already read Campbell Biology. Then, I recommend you to read Alberts' book in the Essential Cell Biology (or Molecular Biology of the Cell if you want to learn very in-depth), and do not study any other branch of biology. Modern biology is studied widely from the molecular and cell aspects, so it is very beneficial to learn the molecular & cell biology first before exploring other subjects.

For general chemistry, I recommend Atkins' Chemical Principles over Oxtoby for rigorous introduction to general chemistry. Both books have strong physical-chemistry flavors, but Atkins has clearer exposition along with good problems. Then, I recommend Hornback or Wade for organic chemistry; they have mechanistic approach, which in my opinion is a proper way to learn organic chemistry. If you like, you can study organic chemistry right after completing first sections of Atkin.

I cannot offer you my advice in physics as it is my weakest area, and I did not study physics as in-depth as other fields I mentioned above.

Most importantly, you should enjoy your Summer! Do physical exercises, enlist in some interesting clubs like boxing club, social activities, etc.!

 

[Calaver]

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). However, I am in high school as well (thus, take everything that I say in stride and listen carefully to the more experienced people around here), and I have had similar "study plans" about a year ago. So perhaps some of my advice, leaning more on the side of mindsets and less on the material, will be beneficial to you.

Don't beat yourself up over not completing the material or achieving your goals. You won't complete all of the material in 5 weeks. But just because you cannot do this does not mean you should feel bad. (Note: In other circumstances, my advice might be slightly different. But you seem to be pretty self-motivated, so I'm not going to worry about you becoming a "bum" in this case.)

In addition, you should realize that in order to be effective, you cannot spend 12 hours a day, 7 days a week toiling over your work (if there is someone that actively does this with the same level of effort that the OP will need to read through all that material, please correct me). Because if you do this, no matter how much you enjoy it in the beginning, it will become absolutely miserable for you once you're on week 3. This video explains well why you can't work too hard. If you think that the greatest scientists worked all day every day on their ideas (much less their textbooks), then you're wrong. If I remember correctly, Paul Dirac (a founder of quantum mechanics and quantum field theory, i.e., a very good physicist) worked 6 days a week and took walks on Sunday in order to clear his head and during one of these walks was when he had one of his key insights (something to do with Heisenberg's matrix mechanics I believe).

In order to study something, especially this many subjects at one time, you should at least have an idea of why you are studying them and in what order to pursue them. Forgive me if I'm wrong, but it seems that you have no clue about either of these matters with regards to what you're studying. The list you gave had no particular order (could be accidental, but I would think that you would plan this out), and you are missing several key subjects (one is vector calculus for electrodynamics) as well as having a few that seem to be extraneous (why are you wanting to learn about partial differential equations and real analysis and complex analysis right now?).

Lastly, I see that you wrote:

I, unfortunately, wasted much of the summer.

What do you mean by "wasted"? If you simply mean not studying, this is a very bad definition of waste. I will bet that many of the things you did were in some sense worthwhile (even if they were just relaxation), so don't consider the time wasted.

I hope that my ramble was in some way helpful to you. Even though you won't be able to accomplish your goal this time, you will eventually (I did in under a year, so it shouldn't take too long) learn how to make reasonable goals. For instance, last fall I was in a similar position as you. Now, I have learned to make more reasonable goals, such as learning a bit of linear algebra over the summer from Shilov plus a few other goals here and there. I still have a lot of fun during my summer, and while I don't work on these things all the time, it is exceedingly enjoyable when I do. At the same time, I have the realization that I probably won't complete my desired sections of all of these by the end of the summer, but that's ok. I still am learning the material well and enjoying myself.

P.S. I think that you could get well into one (maybe two) of the subjects that you are very interested in during the remainder of the summer, and so if you could tell us which one you're most interested in somebody around here probably has a suggestion on a text or website that is good for learning the subject.

 

[bacte2013]

Following up from my advice, I actually think you should not bother studying any field of chemistry except for Atkins for now. Focus on realistic goals, and aim for small achievements.

I like @Calaver's advice.