Lecture:  Tu Th 3:30 pm  4:50 pm at CENTR 115 
Instructor:  Mareike Dressler 
eMail:  mdressler@ucsd.edu 
Office:  AP&M 6444 
Office Hours:  Tu Th 10:00 am  11:00 am at AP&M 6444 
Discussion: 
A01: W 5:00 pm  5:50 pm at HSS 1315, Chuqing A02: W 6:00 pm  6:50 pm at HSS 1315, Chuqing A03: W 7:00 pm  7:50 pm at HSS 1315, Jiajie A04: W 8:00 pm  8:50 pm at HSS 1315, Jiajie 
Teaching Assistant:  Chuqing Shi 
eMail:  chs139@ucsd.edu 
Office Hours:  Tu 5:00 pm  6:00 pm and F 9:00 am  10:00 am at AP&M 1240 
Teaching Assistant:  Jiajie Shi 
eMail:  jis254@ucsd.edu 
Office Hours:  F 2:00 pm  4:00 pm at AP&M 1131 
Credit Hours:  4 (Credit not allowed for both MATH 171A and ECON 172A.) 
Prerequisites:  MATH 18 or MATH 20F or MATH 31AH, and MATH 20C. Students who have not completed listed prerequisites may enroll with consent of instructor. 
Course description:  Math 171A is an upperdivision course introducing students to the field of mathematical optimization, in particular,
the area of linear optimization (historically known as linear programming). Topics covered in this course include the geometry of linear programming,
optimality conditions, the simplex method, duality theory. Some homework assignments will require the use of the package Matlab, although no prior knowledge of Matlab is assumed. Matlab enables the student to concentrate on the fundamental ideas of linear programming without becoming distracted by the rigors of mental arithmetic. The aim of the class is for students to

Textbook:  There is no required textbook for this course. A copy of "Linear Programming Notes" by Philip E. Gill, Walter Murray, and Margaret H. Wright will be made available to enrolled students. Please do not distribute these notes. 
Syllabus:  This website acts as our syllabus. 
Exams: There will be three exams in the class:
⭢ You may use one 8.5 x 11 inch sheet of handwritten notes (which may be written on both sides, no photocopies!). No books, calculators, phones, or other aids may be used during exams.
Homework: Homework will be assigned weekly, and is due on Fridays at 11:00 am, starting in Week 2.
Homework problems will be uploaded on Canvas and Gradescope.
There will be nine (9) homework assignments in total.
The lowest homework grade will be dropped.
There are two methods to determine your course grade. Your grade will be determined using both methods and then the best grade will be used.
A+  A  A  B+  B  B  C+  C  C 

97  93  90  87  83  80  77  73  70 
Notes
Week  Monday  Tuesday  Wednesday  Thursday  Friday 

1 
Jan 07
Overview of the Class: Introduction to Optimization 
Jan 08
Discussion 
Jan 09
Properties of Linear Constraints and Geometry of the Feasible Region 

2 
Jan 14
Properties of the Feasible Region and of the Objective Function 
Jan 15
Discussion 
Jan 16
Two Methods for Toy Linear Programs, FullRank Systems of Linear Equations 
Jan 17
Homework 1 due 

3 
Jan 20
Martin Luther King, Jr. Holiday 
Jan 21
FullRank Systems cont'd, Properties of Incompatible Equations 
Jan 22
Discussion 
Jan 23
Prop's of Incompatible Equations cont'd, Linear Programming with Equality Constraints 
Jan 24
Homework 2 due 
4 
Jan 28
Midterm I 
Jan 29
Discussion 
Jan 30
Optimality Conditions for Equality Constraints, Feasible Directions for Inequality Constraints 
Jan 31
Homework 3 due
Last Day to Drop w/o 'W'


5 
Feb 04
Vertices, Finding a Vertex 
Feb 05
Discussion 
Feb 06
Optimality Conditions for Linear Programming 
Feb 07
Homework 4 due 

6 
Feb 11
Farkas' Lemma and its Implications 
Feb 12
Discussion 
Feb 13
The Simplex Method 
Feb 14
Homework 5 due
Last Day to Drop w/o 'F'


7 
Feb 17
Presidents' Day 
Feb 18
Degenerate Constraints, Mitigating the IllEffects of Degeneracy 
Feb 19
Discussion 
Feb 20
Finding a Feasible Point 
Feb 21
Homework 6 due 
8 
Feb 25
Midterm II 
Feb 26
Discussion 
Feb 27
LPs with Mixed Constraint Types 
Feb 28
Homework 7 due 

9 
Mar 03
LPs in Standard Form, Simplex Method for StandardForm LPs 
Mar 04
Discussion 
Mar 05
Linear Programming Duality Theory 
Mar 06
Homework 8 due 

10 
Mar 10
More Duality Theory, Complexity of Simplex Method 
Mar 11
Discussion 
Mar 12
Other techniques for solving LPs, Applications of Linear Programming, Recap 
Mar 13
Homework 9 due 

11  Mar 17
Final Exam
3:00pm6:00pm 