Tuesday, October 27, 2015

Reordering my Priorities

     Like many college students, I've fell into the trap of trying to keep up academically by neglecting basic needs: health, sleep, hygiene, personal relationships, etc. Not only has this made me more stressed and unsatisfied with myself, I am still struggling with my schoolwork. I thought my problem was bad time management at first, but then I realized that my actions do not reflect my priorities. If someone asked me what they were in order of importance, I'd answer

  1. maintaing physical health 
  2. maintaining mental health
  3. making stronger interpersonal relationships
  4. learning new skills and acquiring knowledge
  5. academic and career success
  6. getting financial independence
  7. enjoying new, exciting experience
     Upon further reflection I realized that my priorities follow along the lines of Masclow's hierarchy of needs:
     This order seems like the best course of action for a fulfilling life.
But my actions in order of effort:
  1. studying
  2. making healthy meals
  3. attending school extra-curricular events
  4. reading self-help books
  5. planning scholarship applications
  6. excercising
  7. connecting with my family
  8. getting enough sleep
  9. making friends
do not reflect my priorities at all. I have tried justifying my impulse to prioritize schoolwork with reasons such as it will open exciting opportunities such as study abroad scholarships and wonderful work in the future. Most importantly, my parents paid thousands of dollars for a college education and it's my responsibility to make the most out of it. However, I've found that putting all this effort into academics has brought little benefit to my life or served any of my other priorities. If I focused on another priority such as health by getting adequate sleep, I would feel better about myself and this would actually improve my academics by increasing my concentration during lecture and improving my memory so I can retain the information I study better.

     I think the reason why I'm working against my personal interests is that I am still in the high school mentality of "get great grades to get great opportunities". I've gotten some perks from my moderate academic success in high school, but I do remember how frustrated and burned-out I was until I started involving more friends in my life and became serious about maintaining my health. I have also learned that this model isn't necessarily true. My professor has told me "good grades are necessary, but not sufficent" at a scholarship meeting. If I want to have as many opportunities open to me as possible, I now know that I need to be an interesting and well-adjusted person in addition to being competent. So, I planned a new course of action:
  1. prioritize getting relaxed before sleeping
  2. interact with my family more
  3. visit my university's counselor
  4. stop stress-eating
  5. break up my long study periods into smaller increments
Hopefully this will give me a healthier work-life balance. After a week or two of trial running, I should be able to determine if this new mindset is a significant improvement from my old one.

Thursday, October 22, 2015

Review: How to Become a Straight-A Student

How to Become a Straight-A Student How to Become a Straight-A Student by Cal Newport
My rating: 4 of 5 stars

Overall, the advice Cal Newport gives is common sense advice that students already get from teachers and parents: don't leave schoolwork until the last minute, always show up for class, take good notes, study a little each day, etc. However, what makes this book very effective is that this advice is coming from straight-A college students who insist that doing all of this will make your college life much more easier and enjoyable. Unlike nagging adults, this book provides the motivational push that students need to start acting. Cal also gives step-by-step advice for challenges such as note taking and passing exams. This book is about maximum results for minimal effort, so these methods will save you time and stress. For me, it helped me manage my procrastinating tendencies and start earning higher grades with no additional effort. But, this book isn't a cure-all for all of my academic problems. I wish Cal included more advice on time management and learning (in addition to the studying) strategies. Even so, this book is definitely a useful guide for current and soon-to-be college students

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Sunday, October 11, 2015

Cross products for Calculus: The Easy Way

After learning both the matrix and the formula method for solving cross products, I found a way to simplify it into 5 easy steps that don't involve excessive memorization and drawing more than 1 matrix. If you are in Calculus II or III, this can save you some time on your exams and homework. This works for cross products of two vectors with three variables each. I haven't been able to figure out if you can take cross products of other types of vectors, so my method might be rather limited.

What is a cross product?

     Very simply, the cross product is one of two ways you can multiply two vectors. When you are asked to find "a x b" you want to get a new vector that is perpendicular to both vectors a and b such as in this picture. The fact that the cross product is "orthogonal" and forms a "right hand triple" with vectors a and b means the same thing.

Now that you know the direction, the next step in understanding the cross product is to find the magnitude.

What is the magnitude?

     Recall that the magnitude of a vector is its norm. For (a x b), ||ax b||=||a|| ||b||sin(θ). Now, remember basic trigonometry where sin(θ) = O/H (opposite over hypotenuse). If you have a parallelogram with a corner angle θ and a side length a, height = asin(θ)

If a is actually a vector and it forms a parallelogram with vector b, you can plug height into ||ab||=||a|| ||b||sin(θ). This gives you ||ab||=||a||*h, which means that the magnitude of  (a x b) is the area of the parallelogram formed by a and b.

How to get the vector answer?

  1. Draw the matrix and set it equal to the vector (i,-j,k) We'll label each column so that it corresponds to its place in the linear combination representation of vectors (ai+bj+ck) This set-up is going to help us solve for each variable (i,-j,k).
  2. To solve for i, cover the i column and multiply the top-left number with the bottom-right number of the uncovered matrix. Draw the first part of the x in the matrix to help you remember.
    Then, you multiply the top-right with the bottom left and draw the second part of the x. You will then subtract the first part with the second part to get i.
  3. For j, you want to cover the j column and multiply the rest of the matrix cross-wise the same way that you would when solving for i.REMEMBER TO MULTIPLY j BY -1 WHEN YOU WRITE DOWN YOUR FINAL ANSWER.
  4. Solve for k by covering the k column and multiplying cross-wise as you would for i.
  5. Simplify and you are done!

Another Great Resource: