Let's avoid the danger zone!
This course provides a framework of core skills in linear algebra, analysis, and vector calculus necessary for data science. There is a focus on improving and developing base skills in programming and engineering mathematics. The teaching language used is Python, however, the skills taught in this course are meant to be language agnostic and applicable to any challenges the data scientist might encounter.
- J. J. Thompson, PhD: [email protected]
- Amy Yuan, MS: [email protected]
Class Location: 44 Tehama St, 3rd Floor, gU Classroom
Class Time: 9:00 AM - 10:30 AM PST, M-T-Th-F
Instructor Assisted Lab Hours: 10:30 AM - 12:00 PM PST, M-T-Th-F
Office Hours - Jared: W 9:00-12:00 PM and by appointment
Office Hours - Amy: After class on lecture days and by appointment
There are four scheduled lectures per week, 1.5 hours each for a total of 6 hours per week contact time. The course runs for 8 weeks. This is to be compared to a standard graduate level 1 semester course with 3 hours per week contact time for 16 weeks. Beyond this, the coursework includes both academic matter (Engineering Mathematics) and practical programming skills. This means that the single course effectively constitutes 2 graduate courses in one. Thus, the student should expect to traverse effectively between 8 and 12 hours exposure time each week. Following the 2 hours study per contact hour rule-of-thumb, this means that the student should set aside approximately 24 additional hours per week of study time above and beyond homework and class assignments. If the student takes a day off, this means that every student should expect to need 4 additional hours after class each day just to keep up
Daily: At the beginning of class every day the class will be given a 10-minute Readiness Assessment Test. This test examines the student's mastery of the course work taught the day before and constitutes a major part of the overall grade (25%).
Lab: The students are regularly given an in-class laboratory exercise exploring the programming topics discussed over the previous two weeks. Graded labs are due the day after they are given (30%).
Take-Home Final: A comprehensive take-home final project is required. Some ideas for a take home project will be provided a little later in the course, although you may begin at any time, subject to the approval of the professor. The project must demonstrate your mastery of the subjects taught in this class. (35%)
Mastery Tracker: Your progress in the class will be tracked by notations in the mastery tracker (learn.galvanize.com). The mastery tracker grades reflect the instruction team's best assessment of your skill level in the given proficiency. These notations can change up or down dependent on your performance in the class. Your mastery tracker score is only counted towards your final grade. (10%)
Final grades will be curved somewhat so as to reflect standard procedures relative to the UNH graduate school.
Material sufficient to have an understanding of what is taught here is provided by the instructors in the form of lecture notes. Class lectures will be given in a format closely following the notes prepared by the lecturer.
We will be working from one primary textbook:
Erwin Kreyszig's Advanced Engineering Mathematics, 9th ed.
The textbook is expensive but can be rented online from Amazon for little money.
It is strongly recommended that the student purchase their own copy of the text and the student solutions and study manual so that they have something to practice out of and work from.
Additionally some material will be covered from:
J. Marsden and A. Tromba's Vector Calculus, 4th ed.
It is not necessary to own this book, but it can be useful to have.
- Solve linear systems of equations and determine linear independence.
- Solve problems using vector spaces, linear transformations, distance metrics, norms etc.
- Diagonalize matrices and obtain singular value decomposition of matrices.
- Formulate and solve fundamental problems using vector calculus.
Students are expected to be present and on time for all class meetings.
Cell phones can be highly disruptive to the class environment. Please silence these devices. In the event of an emergency, please step out of the classroom.
You will learn more easily and enjoyably if you actively participate verbally and stay engaged. The lecturer will "call out" individual students to participate in answering questions as given in class. Students are advised to maintain a high level of preparation so as to smooth these interactions.
This course is divided into five units:
- A review of Linear Algebra
- Plotting, Norms and Solving Vector Based Problems
- A Review of Vector Calculus
- Lagrange Multipliers
- Application of Mathematical Concepts to Programming
As per the University's Academic Integrity Policy and Procedures:
The University expects that all students, graduate and undergraduate, will learn in an environment where they work independently in the pursuit of knowledge, conduct themselves in an honest and ethical manner and respect the intellectual work of others. Each member of the University community has a responsibility to be familiar with the definitions contained in, and adhere to, the Academic Integrity Policy. Students are expected to maintain the highest standards of academic integrity.
Violations of the Academic Integrity Policy include (but are not limited to):
- Cheating -- i.e. Don't read off of your neighbors exams
- Collusion -- Group work is encouraged except on exams. When working together (on exercises, etc.) acknowledgement of collaboration is required.
- Plagiarism -- Reusing code presented in labs and lectures is expected, but copying someone else's solution to a problem is a form of plagiarism (even if you change the formatting or variable names).
Dishonesty will result in administrative action and a grade of "F" in this course.
Monday, Tuesday, Thursday, Friday except for holiday schedules, which will be announced as relevant
| Time | Activity |
|---|---|
| 9:00-10:30 | Lecture |
| 10:30-12:00 | Lab |
These are the instructor supported class hours. Instructors may be available on a case-by-case basis afterhours by appointment.
Tentative Curriculum:
| Session | Lesson # | Topic | Instructor |
|---|---|---|---|
| LA | 1.1 | Introduction to class and Introduction to Matrices and Vectors | Jared |
| LA | 1.2 | Matrices as Systems of Equations | Amy |
| LA | 1.3 | Linear Independence, Existence and Uniqueness | Amy |
| LA | 1.4 | Determinants and Invertibility | Jared |
| LA | 2.1 | Vector Spaces and Transforms | Amy |
| LA | 2.2 | Eigenvalues and Eigenvectors | Jared |
| LA | 2.3 | Review/Cushion Day | Jared |
| LA | 3.1 | Basis and Change of Basis | Jared |
| LA | 3.2 | Diagonalization | Jared |
| LA | 3.3 | The Dimension Theorem | Amy |
| LA | 3.4 | Singular Value Decomposition | Jared |
| LA | 4.1 | A Review of Vector Geometry I | Amy |
| LA | 4.2 | A Review of Vector Geometry II | Amy |
| LA | 4.3 | Construction of Basis | Jared |
| LA | 4.4 | Rotations into New Basis | Jared |
| LA | 5.1 | The Fundamental Theorem of Linear Algebra | Jared |
| LA | 5.2 | Review/Cushion Day | Jared |
| VC | 5.3 | Limits, Derivatives, and Vector Derivatives | Amy |
| VC | 5.4 | The Chain Rule and Total Derivative | Amy |
| VC | 6.1 | The Del Operator | Jared |
| VC | 6.2 | Problems in Vector Geometry | Jared |
| VC | 6.3 | The Extreme Value Theorem | Jared |
| VC | 6.4 | Review/Cushion Day | Amy |
| VC | 7.1 | Lagrange Multipliers I | Jared |
| VC | 7.2 | Lagrange Multipliers II | Jared |
| VC | 7.3 | Norms/Metrics and the Unit Circle | Amy |
| VC | 7.4 | Review Day | Jared & Amy |