PHY315
D MATH TOOLS FOR PHYSICS
“Learning
math is like swimming – you’ve got to get your feet wet!”
Time:
M W F
11:15-12:05 PM
Place: Knight Physics Building 203
Instructor: Professor
Neil Johnson, PhD (Harvard), MA (Camb)
http://www.physics.miami.edu/~njohnson/
njohnson@physics.miami.edu
Office: Knight Physics Building, office
307
Office Hours: TBA
Teacher Assistant: TBA
Welcome!
I am going to try to make this math-for-physics course the one
I wish had had, but didn’t. All physics courses at all universities, everywhere
in the world, tend to have a ‘math-for-physics’ course such as this – but they
often come across as being too dry, too abstract … and sometimes downright
boring. The one I took definitely was of this type. In fact, it nearly led me
to give up Physics – which actually brings me to a crucially important point:
Irrespective of where your career takes you
(whether within conventional physics or outside in finance,
business, medicine, engineering etc.)
the concepts and techniques in this course will at some stage
prove very useful.
I can’t count how many friends and former students
that I have had, who have been in interviews at Wall Street banks where they
are asked something about the techniques discussed in this course. I even know
of someone working as a computer graphics designer, who was grilled on vector
analysis at his interview with a large well-known media corporation. So in
short, this material is crucial if you stay in physics and if you decide to leave physics – and equally so. So you should make your best possible
efforts to ace this course!
My
challenge is to liven the material up at the same time as
getting the techniques and concepts across -- just like a music teacher will
hopefully try to add some fun to learning scales, or a sports trainer will add
some fun to repetitive exercises. My daughter happens to swim, and has to do
endless pool lengths every day – but her trainer makes it fun. My challenge is
to do the same for you with this course.
Your
challenge
is to attend every class, do every exercise, go back and re-do exercises you
couldn’t finish or didn’t fully understand (even after they are graded) and ask
every question that occurs to you. In my opinion, there is no such thing as a
dumb question -- the only thing which is truly dumb is to stay silent when you
are stuck!
So how we will
each overcome our respective challenges? Our secret weapon comes in the form of
a truly outstanding piece of tutorial writing: Professor Nearing’s amazing
online book which includes all the
material in this course. In fact, it includes far more than we have time to
cover – but we will do our best. The precise topics to be included will be
clarified as the course progresses, based on how quickly you assimilate the material.
Ideally, we would cover the whole book since it is all great stuff!
So what should you do now? You should
immediately download Prof. Nearing’s online book from
http://www.physics.miami.edu/~nearing/mathmethods/
and start reading through the Introduction on page
iii. In fact, his Introduction is packed with incredibly valuable advice. Note
that his book is free, and can be downloaded multiple times in various
formats. In fact I am hoping that you read it so much that you have to print
multiple copies throughout the semester simply because you have worn out
previous ones. In short, you should aim to ‘sleep, dream, and eat’ this book.
Trust me, you won’t regret it.
Please note: You must bring a copy of this book, or
at least the portions of it that we are looking at, to every class. They ARE
the course notes, and our classes will be focused explicitly on this material.
There will be no other formal notes or handouts.
In terms of the mechanics of learning, the key is
practice, practice, practice. Hence this class will be dominated by
problem-solving. My experience is that noone really learns from a general
mathematical formulation of a topic – instead, they learn by example. So we will have a quick quiz almost every
class, plus there will be regular homeworks, tests, midterm and a final. In
addition, I will regularly ask students to present solutions to problems on the
blackboard during class, in front of the class. This isn’t because I like to
inflict such things on you, or that my secret hobby is grading – it is because
we don’t learn by simply listening and reading. We have to get our feet wet.
Setting and meeting
deadlines is an important professional skill.
I expect you to either meet these deadlines or set alternative deadlines
with me in advance. College is an
important time to develop a reputation as someone who gets things done, and
gets things done on time. Grades will be
penalized for late work.
Anticipated Grade Weight Summary
(Any changes will be announced in
class as the course progresses)
|
Evaluation |
Percentage |
|
Class quizzes,
presentations, tests |
30% |
|
Homeworks |
30% |
|
Midterm |
15% |
|
Final |
25% |