University of Florida

ABE 6933
FOUNDATIONS OF PROBABILITY AND MATHEMATICAL STATISTICS: A SCIENTIFIC COMPUTING APPROACH

Semester Taught - Spring

Catalog Description

Credits: 3

This course is a fast-paced introduction to calculus-based probability and statistics aimed at graduate students in engineering and quantitative life sciences. It covers the essentials of STA5325 and STA5328 in a single semester making use of calculus and basic scientific computing to gain understanding about fundamental results and methods of probability and statistics. Successful completion of the course will enable one to take graduate-level courses in statistics, biostatistics, operations research and computer science. Whenever possible, the course prioritizes development of intuition behind statistical methods via scientific computing and simulation experiments rather than formal derivations and justification of the procedures. R will be the preferred statistical computing environment of choice; Matlab will also be allowed.
Successful completion of this course (or a sequence STA5325/5328) will be a prerequisite for students wishing to take any of my future topics courses.

Pre-requisites/Co-requisites

  • solid knowledge of calculus of multiple variables;
  • experience reading and writing simple computer programs in a scripting language (ideally, in R); basic knowledge of scientific computing (e.g., ABE 5643C for ABE students);
  • intro undergraduate statistics; a recent first graduate statistical methods class (such as ALS5932 or STA6166) is preferred

Course Objectives

  • learn essentials of calculus-based probability theory with an aid of computer experiments
  • apply the knowledge of probability to understand fundamental principles, methods and results of mathematical statistics
  • integrate knowledge of probability, statistics and scientific computing to make exact and simulation-based inference in a modern computing environment

Instructor

Nikolay Bliznyuk
Office: Room 239 Rogers Hall
Phone: 392-1864
Email: nbliznyuk@ufl.edu

Material/Supply Fees

None.

Class Materials Required

lecture notes and readings will be posted on course page. R and R Studio environments are available free of charge.

Course Outline

Topics

We shall cover most topics in the course text (please check out the table of contents).
Tentative list of topics

  • Basic Probability: random events, calculus of probability.
  • Discrete Random Variables and Their Probability Distributions. 
  • Continuous Random Variables and Their Probability Distributions.
  • Multivariate Probability Distributions.
  • Functions of Random Variables.
  • Sampling Distributions and the Central Limit Theorem.
  • Point and Interval Estimation. 
  • Properties of Point Estimators and Methods of Estimation.
  • Hypothesis Testing.
  • Linear Models and Estimation by Least Squares. 

Grading

Attendance and participation in class is expected. Make-ups are not allowed except for documented health, family emergency or work reasons; details of make-ups – to be arranged with the instructor in advance of the event.

90-100 A
87-89 B+
80-86 B
77-79 C+
70-76 C
<70 D
Three exams 60%, weighted equally
(two prelims and the final – potentially, take-home)
Homework 40%
(problem sets, potentially graded through quizzes, TBA in advance)

Academic Honesty

As a student at the University of Florida, you have committed yourself to uphold the Honor Code, which includes the following pledge: “We, the members of the University of Florida community, pledge to hold ourselves and our peers to the highest standards of honesty and integrity.”  You are expected to exhibit behavior consistent with this commitment to the UF academic community, and on all work submitted for credit at the University of Florida, the following pledge is either required or implied: "On my honor, I have neither given nor received unauthorized aid in doing this assignment." 
 
It is assumed that you will complete all work independently in each course unless the instructor provides explicit permission for you to collaborate on course tasks (e.g. assignments, papers, quizzes, exams). Furthermore, as part of your obligation to uphold the Honor Code, you should report any condition that facilitates academic misconduct to appropriate personnel. It is your individual responsibility to know and comply with all university policies and procedures regarding academic integrity and the Student Honor Code.  Violations of the Honor Code at the University of Florida will not be tolerated. Violations will be reported to the Dean of Students Office for consideration of disciplinary action. For more information regarding the Student Honor Code, please see: http://www.dso.ufl.edu/sccr/process/student-conduct-honor-code.  

UF Counseling Services

Resources are available on-campus for students having personal problems or lacking clear career and academic goals which interfere with their academic performance. These resources include:

  1. University Counseling Center, 301 Peabody Hall, 392-1575, personal and career counseling;
  2. Student Mental Health, Student Health Care Center, 392-1171, personal counseling;
  3. Center for Sexual Assault/Abuse Recovery and Education (CARE), Student Health Care Center, 392-1161, sexual assault counseling;
  4. Career Resource Center, Reitz Union, 392-1601, career development assistance and counseling.