Syllabus for
a. Math 488P - Probability and Statistics for Educators
b. Math 588 - Probability and Statistics (MAT/MST)
Spring 2015

Last update: March 24, 2015 - 10:35 AM

Instructor Section Meeting
Michael Fochler, WH 130
      Office hours: Mon 1:15 - 3:00,     Thu 2:30 - 4:00
      mfochler@math.binghamton.edu 		Section 01 Mon, Thu 5:40-7:40 OW-100E

Welcome to Math 488P/588, Probability and Statistics for Educators and MAT/MST. This is the syllabus for this course. Here is the most important link:

Home page for Math 488P/588:

The Math 488P/588 home page is currently just a skeleton. Over time it will be the web page you visit most frequently as your home work assignments and general announcements will be posted here rather than on Blackboard.

PREREQUISITES:

Math 222 (Calculus 2): If you did not pass Math 222 this does not automatically disqualify you but you must see me asap! You need some Calculus background later in the course and you may have to catch up on some topics to understand the material. You will be dropped from this course unless you can convince me that you have knowledge or are able to learn quickly about limits, power series and integration.

Course Material:
Textbook:
    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.
    ----------
Additional course material:
    The following documents are also referenced in class.
   
  1. 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.
  2. 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.
  3. 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!
    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.
   
  1. 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.
  2. 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:
    • Ch. 1.11. Set Identities: Everything starting with ``Proof 2'' until the end on p.105
    • All of Ch. 1.15. Computer Representation of a Set (i.e., the remainder of the document).
  3. 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
  4. 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.
  5. 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:
    • All of Ch. 1.6. Examples of equivalence relations EXCEPT it last three lines on p.7 (definition of a fiber over f(x)).
    • All of Ch. 1.7. Extra: composition of relations.
  6. 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.

Course content:

There are several themes to this class and they will be taught intermittently:

  • Theme 1: Experience how probability and statistics is taught at an entry level: The Bluman book is not really above the level of mathematical sophistication of a Precalculus or AP Calculus or AP Statistics level. This comes from a non-expert as far as high school math teaching is concerned but from my experience with my son's precalculus text book and tutoring high school students the major differentiator between a 100 level course in descriptive statistics and those high school classes is the difference in speed with which this material is being taught.
  • Theme 2: Additional background in probabilistic modeling that allows you give explanations to your students beyond what you happen to see in their textbooks: Bluman has little to offer beyond rolling dice, flipping coins and picking cards. You will learn more about mostly discrete probability models but also enough about continuous random variables to understand the normal distribution and why (x̄ - μ)/σ can be looked up as a z-score if the sample size is big enough.
  • Theme 3: The interplay between probabilities and statistics.
    • Sample mean and sample standard deviation as random variables.
    • How random sampling relates to independent random variables.
    • The Bayes rule.
    What You learn here will be very short on theory
  • Theme 4: Some random phenomena that involve limits.
    • Law of Large Numbers and Central Limit Theorem.
    • Exponential and Poisson random variables.
    • The Poisson process.
    What You learn here will be very short on theory

Aside from a few simple rules for the computation of random variables, no proofs will be given for any of those topics. Rather, you are expected to understand the meaning of the definitions and theorems.

How to succeed in this course:

You are advised to attend class regularly as there will not be notes for some of the material I am going to teach. Work through the material presented in class and do the reading and homework assignments.

It is your responsibility to keep informed of all announcements, syllabus adjustments, or policy changes, regardless of whether they were made by email, on Blackboard, or during class.

The material of the text can easily be taught to non-math majors in their first semester but the additional material that I am supplementing it with requires a deeper level of thinking.

If it has been a while since you took calculus, look up the chapters on infinite series and improper integrals.

Homework:

Homework will be assigned for almost every class. Some or all of it will be graded. What homework I collect for grading will be not be announced in advance. You are expected to bring all your homework to class when it is due.
Homework and quizzes together will account for 20% of your grade.

Quizzes:

Quizzes will be given occasionally and they will not be announced in advance.
Homework and quizzes together will account for 20% of your grade.

Tests:

There will be two tests. The dates are:

  • Test 1 (100 points): Thursday, March 19
  • Test 2 (100 points): Thursday, April 16

Final exam:

The final exam was originally scheduled for Friday May 15, 2015   -   Time: 3:15 - 5:15 PM. The students requested unanimously to have it moved to an earlier date. This is the new date and time for the final exam of this course:
Monday May 11, 2015   -   Time: 8:05 - 10:05 PM   -   Location: WH 329 (Math building).
The time for all finals is set by the registrar and is not flexible. Do not make travel arrangements that will have you leave campus prior to the exam.

The final exam is worth 35% of your grade. The final exam is comprehensive, covering most of the material in the course. Details as to what specific material will be excluded will be given at least two weeks before the end of the semester.

Makeup quizzes and exams:

If you will be absent from a test (not a quiz) for a legitimate reason, you must notify me before the date of the test and provide documentation of your excuse. If you have a last minute emergency, you must e-mail me ASAP. Do NOT wait until the following class. A make-up will be given only if you provide valid documentation of your absence and you contact me before the following class.

There will be no make-up quizzes unless you were hospitalized or there was a family emergency of a very severe nature. You must provide valid documentation of your absence and contact me before the following class.

Special rules apply to the final exam: If you have a university conflict with other final exams (another exam scheduled for the same time, or three exams within a 24 hour period) you are entitled to have one of your exams rescheduled. If you have such a situation and wish to take the Math 488P/588 make-up final, you must notify me in writing (email is fine) by Friday, May 1. The date and time of the make-up final and its location have not yet been determined as I am trying to find out whether I can give the final before graduation day. If you do not notify me by the deadline it is unlikely that you will be accommodated. YOU MUST NOTIFY ME BY THE DEADLINE IF YOU WISH TO TAKE THE MAKE-UP EXAM. YOU CANNOT "JUST SHOW UP."

Grading policy:

The following is not 100% finalized but revision is not very likely:

  • Homework and quizzes: 20%
  • Test 1: 10%
  • Test 2: 10%
  • Final: 35%
  • Project: 25%

Academic Honesty:

All students are expected to adhere to the Student Academic Honesty Code. You are required to write your own homework solutions. You may not use another student’s work as a "model" and you must not allow other students to use your work.

Best wishes for a successful semester!

Michael Fochler