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Course Material for Math 488P / Math 588
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Course Material:
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Textbook:
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Elementary Statistics - A Step by Step Approach - A Brief Version,
7th Edition
by Allan G. Bluman (McGraw-Hill, 2013) - referenced as "Blu".
The "Cookbook approach to doing statistics" part of the course
will follow to a large degree the textbook.
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Additional course material:
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The following documents are also referenced in class.
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Principles of Statistics (Dover Books on Mathematics)
by M.G. Bulmer - referenced as "Bulmer"
This book is more mathematically oriented and I shall refer to it for items
beyond the scope of the text book. It is written in a very arcane way and
primarily useful for you to study statisics topics explained in class which are
not to be found in the Bluman text. It has a very interesting discussion of the
different manisfestations of probability but it describes "practical" tools of
statistics such as the setup of histograms (slightly) different from Bluman.
As far as homeworks, quizzes and exams are concerned, you must follow the Bluman book.
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Math 382 Lecture Notes - Probability and Statistics
(Jan 8, 2013) - referenced as "H/M"
by Anwar Hossain and Oleg Makhnin
I found this resource on the internet and this will be your primary
resource concerning probability. Homework, quizzes and tests about
probability (as opposed to applying statistical methods)
will be given at this level of sophistication. I shall indicate
in class how to resolve conflicts in notation and definitions
when they occur.
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Lecture Notes in Probability
(April 5, 2009) - referenced as "Ku"
by Raz Kupferman
I found this resource on the internet and I shall reference only
very few selected topics .
Its very limited purpose is to give you a resource for certain definitions
and some theorems that I only make part of this course because they
allow you get a better conceptual understanding.
Primary example: σ-algebras as holders of the probabilistic info
associated with a random variable.
Be not discouraged if you look at this document and you feel it is way over your head:
These are the lecture notes for a graduate level course in probability!
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All of you have taken Math 330 and I proceed in my lectures accordingly
I assume you all still have the yellow (Springer textbook from
Beck/Geoghegan (The Art of Proof).
Here are some documents that give you an intro to sets of functions which
I believe are, with the possible exception of the Pete Clark lecture notes
on relations and functions, much gentler as they give many examples.
I have copied those documents from a 330 course that was taught
earlier by Prof. Marcin Mazur.
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Sets part 1:
This document is a very basic introduction to sets which
you should be able to skim through in a hurry.
You should skip nothing and be sure you understand
all examples.
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Sets part 2:
This document covers to a large degree the same material as
Sets part 1:
Again, many of you should be able to skim through in a hurry.
and again, be sure you understand all examples.
You can skip the following:
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Ch. 1.11. Set Identities:
Everything starting with ``Proof 2'' until the end on p.105
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All of Ch. 1.15. Computer Representation of a Set
(i.e., the remainder of the document).
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Functions part 1:
This document is very brief and it will probably take you more time
per page to study it. You can skip
chapter 2.4. Floor and Ceiling Functions. Note that I have an important
comment on the use of f - 1(y) for both the inverse image (a set!)
of y and the image of y under the inverse function f - 1 of f
here
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Functions part 2:
This document focuses on injective, surjective and bijective
(invertible) functions.
Pick up your copy of Stewart's Calculus and review the chapter on inverse functions.
You will see material on injective functions (Stewart calls them one-to-one)
and on inverse functions. This will help you understand the document.
Skip all proofs as the important ones are given in B/G. but be sure to understand
the definitions and examples and draw pictures with functions that you understand
well to get a feeling for why the theorems are true.
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Lecture Notes:
on Relations and Functions by Pete Clark.
This document is very tersely written and you should read it several times after
you have digested the material of the above-mentioned write-ups on sets and
functions. The entire chapter 2 on functions is especially important.
Do not try to understand the proofs but, as always, try to understand the
examples but draw pictures with functions that you understand
well to get a feeling for why the theorems are true.
Pay special attention to the last paragraph on p.5 in
Ch. 1.5., The partition determined by an equivalence relation.
It clarifies that a set does not contain duplicates:
you can list an element x as often as you like. This will not alter the set!
Besides the proofs you can skip the following:
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All of Ch. 1.6. Examples of equivalence relations
EXCEPT it last three lines on p.7 (definition of a fiber over f(x)).
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All of Ch. 1.7. Extra: composition of relations.
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Lecture Notes:
Direct and Indirect Image
I am the author of this document.
For that reason it is much more likely to contain errors than the ones
listed above as those have probably been vetted by many viewers
before having been made accessible on the internet.
Caveat emptor!
This document will be added to in the future.
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