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Welcome to Mathematical Methods For
Quantitative Finance.

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For this first video, I'm just going to do
a

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quick overview of what you can expect
during this course.

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So, I'm your instructor Kjell Konis.

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First name rhymes with cello, so cello
without the o.

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For evaluation for this course, this is
something

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I can't do really well in a massive
setting.

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So what I've come up with are discussion
questions.

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And so, at the end of each video, there
will be a discussion question.

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It should be something that if you've
understood the

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video that you'll be able to answer just
within a few minutes.

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And then you're encouraged to share your
solution on on the forum.

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And so hopefully, sort of just
organically,

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there'll be some correct crowd sourced
solutions.

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And additionally, there'll be weekly
homework assignments.

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And these will be something, these will be
more difficult problems.

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So the idea will be that you watch all of
the

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videos for one particular week, and then
you

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should be able to do the homework
assignment.

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It should take you probably 3 or 4 hours,
about

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the same amount of time as the videos take
to watch.

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And then there will be a due date for
these

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homework assignments, and after the due
date, I will post solutions.

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And again, because it's a mathematics
course, it's going

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to be something that's difficult for me to
actually grade.

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So, you'll be expected

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to just go through the solutions and grade
yourself.

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And then one last thing I, I want to
mention

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at the very beginning, is Wolfram/Alpha,
this is a website.

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It's a lot like Google, except

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it's for asking and answering mathematics
questions.

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A lot of what would normally be in a first
year calculus

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course or a first year linear algebra
course is some rote memorization.

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So there're just certain functions where
you

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have to memorize this is the derivative

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of that.

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I don't really want to concentrate so much

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on just having you memorize things like
this.

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So you can, and there are a lot of tools
on line now.

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So my favorite right now is Wolfram Alpha.

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And so, for simple functions, things like
sine, cosine, logarithm, you can

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just ask Wolfram Alpha, and just type into
the, into the search bar.

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You know, what is the derivative of the
logarithm and it'll think for

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a couple seconds, and it'll give you the
answer.

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So what the course is going to cover.

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So, the numbers on the left here, these
correspond to the weeks of the course.

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So this will be an eight week course.

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The first week is going to be a review of
limits and derivatives.

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The second week will be integration.

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So, this is going to be essentially a two
week review

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of what you would normally learn in a
first year calculus course.

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And then, we'll move onto partial
derivatives.

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And so, partial derivative is something
you

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can take using the same techniques that

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we'll cover in week one, but it's defined
for a function of several variables.

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And then multiple integrals, week 4, is
the same idea except for integration.

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So, it's basically how you can make sense

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of integrals of functions that take
several variables.

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And the reason these topics are, are sort
of divided into two

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bunch, bunches, so we have one through
four and then five through eight.

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What I'm really aiming for with the first
four weeks is I want, I

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want you to be able to take

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the derivatives of the Black Shoal's
pricing formula.

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And since this is a math class, really
what I'm

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going to be focusing on is the mathematics
of this.

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So, the Black Shoals formula is just
function of many variables.

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And so, if you understand the, the
concepts

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that are, that we're going to cover in
these

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first 4 weeks, then you're going to be
able

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to take the derivative of the Black Shoals
formula.

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And these derivatives are something that's
commonly known as the Greeks.

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The second set of lectures is going to be
on linear algebra, Legrange

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multipliers and numerical methods.
And the,

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the problem I'm looking at in this second
set of the course

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is something called minimum variance
portfolio.

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And so it'll turn out is, when we look at
linear algebra,

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we're really going to be concerning
ourselves

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with solving systems of linear equations.

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Lagrange multipliers is going to give us
the

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tools we need to calculate the minimum.

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So we want to find a portfolio of assets
that has the minimum variance.

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And then it's going to turn out that when
we use this Lagrange multiplier approach,

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it's going to give us a system of linear
equations that need to be solved.

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So, we'll have done that already in weeks
five and six.

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And then finally in week 8, I'm going to

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start using something called the R
Environment for Statistical Computing.

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It's, software program

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for working with vectors and matrices, and

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also, for it's also a programming
language.

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It's something very similar to MATLAB, if

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you already have some experience with
that.

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And we'll actually try and solve some
problems using a computer to do that.

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So there's one recommended textbook for
this

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course, it's Primer for the Mathematics

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of Financial Engineering by Dan Stefanica.

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This is a very a much more general book
than, than this course will be.

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So this book contains several mathematical
topics as

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well as the financial applications of
those topics.

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I'm going to just choose a few of the
mathematical topics and

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I'm going to focus much more on just the
mathematics and not so much

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on the, on the financial applications.

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And the idea being that after you do this
course, you'll be a lot ready, better

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prepared to go on to a course where

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they're going to focus more on the
finance.

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And it'll be sort of like you, you sort of
learn one thing first and then the other.

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And the idea being that will be a bit
easier for you

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than trying to learn both the mathematics
and the finance in tandem.

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And one thing that's nice about this
course,

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is there's also a solutions manual which
has detailed

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solutions for all of the homework
assignments in this book.

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And so, I, I recommend if you, if you can
get your

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hands on the textbook, that you also try
and get the solutions manual.

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And then on your own time, try and work

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through some of the, the exercises in in
the textbook.

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And then use the solutions manual to make
sure that

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you're using the right approach and
getting the right answer.

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And the last recommended book that I
wanted to mention.

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So this is the first year calculus book

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that they use at the University of
Washington.

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And so that's why I've put it on this
slide and have a picture of it.

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But really any first year calculus book
will be

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sufficient, and this one is over a
thousand pages long.

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And really what you're looking for is just
sort of and encyclopedia of calculus.

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So that when you have questions,

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you have somewhere to go and look it up.

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So, Calculus, Early Transcendentals by
James Stewart.

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pretty much any edition would be
sufficient,

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or any other first year calculus book.

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But if you get your hands on a book like
that, that is going

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to be a valuable resource for doing some
of the exercises in this class.

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Okay?

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So that's all I have for the introduction,
and

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I hope you enjoy the rest of the course.