[PDF] Math 254: Introduction to Linear Algebra

1 Math 254: Introduction to Lecture Notes #1 Introduction Peter Blomgren, Department of Mathematics and Statistics Dynam...

The Professor The Class — Overview The Class... Linear Algebra

Math 254: Introduction to Linear Algebra Lecture Notes #1 — Introduction Peter Blomgren, [emailprotected] Department of Mathematics and Statistics Dynamical Systems Group Computational Sciences Research Center

San Diego State University San Diego, CA 92182-7720 http://terminus.sdsu.edu/

Fall 2016 Peter Blomgren, [emailprotected]

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The Professor The Class — Overview The Class... Linear Algebra

Outline 1

The Professor Academic Life Contact Information, Office Hours Non-Academic Life

The Class — Overview Literature & Syllabus Student Learning Objectives Grading Expectations and Procedures

The Class... Resources Formal Prerequisites Course Technology and Resources

Linear Algebra The What? Why? and How?

Peter Blomgren, [emailprotected]

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The Professor The Class — Overview The Class... Linear Algebra

Academic Life Contact Information, Office Hours Non-Academic Life

Academic Life

MSc

MSc. Engineering Physics, Royal Institute of Technology (KTH), Stockholm, Sweden. Thesis Advisers: Michael Benedicks, Department of Mathematics KTH, and Erik Aurell, Stockholm University, Department of Mathematics. Thesis Topic: “A Renormalization Technique for Families with Flat Maxima.” q=1/2 0.1 0.08 0.06 0.04 0.02 0 -0.02 -0.04 -0.06 -0.08 -0.1 0.5

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Figure: Bifurcation diagram for the family fa, 1 [Blomgren-1994] 2

Peter Blomgren, [emailprotected]

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The Professor The Class — Overview The Class... Linear Algebra

Academic Life Contact Information, Office Hours Non-Academic Life

Academic Life

PhD

PhD. UCLA Department of Mathematics. Adviser: Tony F. Chan. PDE-Based Methods for Image Processing. Thesis title: “Total Variation Methods for Restoration of Vector Valued Images.” The Noisy Space Curve

The Recovered Space Curve

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Figure: The noisy (SNR = 4.62 dB), and recovered space curves. Notice how the edges are recovered. [Blomgren-1998]

Peter Blomgren, [emailprotected]

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The Professor The Class — Overview The Class... Linear Algebra

Academic Life Contact Information, Office Hours Non-Academic Life

Academic Life

Postdoc

Research Associate. Stanford University, Department of Mathematics. Main Focus: Time Reversal and Imaging in Random Media (with George Papanicolaou, et. al.) 1

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Figure: Comparison of the theoretical formula for a medium with L = 600 m, ae = 195 m, γ = 2.12 × 10−5 m−1 . [Left] shows a hom*ogeneous medium, γ = 0, with a = 40 m TRM (in red / wide Fresnel zone), and a random medium with γ = 2.12 × 10−5 (in blue). [Right] shows γ = 0, with a = ae = 195 m (in red), and γ = 2.12 × 10−5 , with a = 40 m (in blue). The match confirms the validity of [the theory]. [Blomgren-Papanicolaou-Zhao-2002] Peter Blomgren, [emailprotected]

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The Professor The Class — Overview The Class... Linear Algebra

Academic Life Contact Information, Office Hours Non-Academic Life

Academic Life

Professor

Professor, San Diego State University, Department of Mathematics and Statistics. Projects: Computational Combustion, Biomedical Imaging (Mitochondrial Structures, Heartcell Contractility, Skin/Prostate Cancer Classification). 20

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Figure: [Left] Phase-space projections produced by the time coefficients of the POD decomposition of the rotating pattern shown in [Right]. [Blomgren-Gasner-Palacios-2005]

Peter Blomgren, [emailprotected]

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The Professor The Class — Overview The Class... Linear Algebra

Academic Life Contact Information, Office Hours Non-Academic Life

Contact Information

Office Email Web

Phone Office Hours TA Office Hours SI Hours

GMCS-587 [emailprotected] http://terminus.sdsu.edu/SDSU/Math254/ http://webwork.sdsu.edu/webwork2/math-254-blomgren/ https://blackboard.sdsu.edu/ n/a MTuW: 1:30pm – 3:00pm and by appointment. Trevor Hawkins: GMCS-528, Tu 10:00am – 1:00pm. TBA.

Peter Blomgren, [emailprotected]

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The Professor The Class — Overview The Class... Linear Algebra

Academic Life Contact Information, Office Hours Non-Academic Life

Fun Times... ⇒ Endurance Sports

Triathlons: (12) Ironman distance (2.4 + 112 + 26.2) — 11:48:57 (16) Half Ironman distance — 5:14:20

[PR]

Running (1) 100k Race (62.1 miles) — 15:37:46 (1) Trail Double-marathon (52 miles) — 10:59:00 (5) Trail 50-mile races — 9:08:46 (6) Trail 50k (31 mile) races — 5:20:57 (15) Road/Trail Marathons — 3:26:19 (7:52/mi) (24) Road/Trail Half Marathons — 1:36:25 (7:21/mi) Peter Blomgren, [emailprotected]

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The Professor The Class — Overview The Class... Linear Algebra

Literature & Syllabus Student Learning Objectives Grading Expectations and Procedures

Math 254: Literature

“Required” — Linear Algebra with Applications, 5th Edition, Otto Bretscher, Pearson, 2013. ISBN-10: 0-321-79697-7; ISBN-13: 978-0-321-79697-4 “Required” — (Supplemental) Class notes and class web-page. “Can I Use a Different Edition of the Book?!” — Probably, but publishers tend to like to move things around to make it harder to use old(er) editions; so I’m not sure it’s worth it?

Peter Blomgren, [emailprotected]

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The Professor The Class — Overview The Class... Linear Algebra

Literature & Syllabus Student Learning Objectives Grading Expectations and Procedures

Math 254: Introduction — What we will cover

1 — Linear Equations A — Vectors B — Techniques of Proof 2 — Linear Transformations 3 — Subspaces of Rn and Their Dimensions 4 — Linear Spaces 5 — Orthogonality and Least Squares 6 — Determinants 7 — Eigenvalues and Eigenvectors

Peter Blomgren, [emailprotected]

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The Professor The Class — Overview The Class... Linear Algebra

Literature & Syllabus Student Learning Objectives Grading Expectations and Procedures

Math 254: Student Learning Objectives

[OLD]

To gain familiarity with, and mastery of, the fundamental building blocks of Linear Algebra: — Matrix algebra, Gaussian elimination, determinants, vector spaces, linear transformations, orthogonality, eigenvalues, and eigenvectors.

Peter Blomgren, [emailprotected]

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The Professor The Class — Overview The Class... Linear Algebra

Literature & Syllabus Student Learning Objectives Grading Expectations and Procedures

Math 254: Student Learning Objectives

[NEW]

One “model” for learning is Blooms Revised Taxonomy(∗) , where we have 2 “dimensions:” Cognitive Process 1 2 3 4 5 6

remember understand apply analyze evaluate create

Knowledge 1 2 3 4

factual conceptual procedural metacognitive

The goal of learning is to go “deeper” in both categories! (∗) Adopted from: Anderson, Lorin W., David R. Krathwohl, and Benjamin Samuel Bloom. A taxonomy for learning, teaching, and assessing: A revision of Bloom’s taxonomy of educational objectives. Allyn & Bacon, 2001.

Peter Blomgren, [emailprotected]

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The Professor The Class — Overview The Class... Linear Algebra

Literature & Syllabus Student Learning Objectives Grading Expectations and Procedures

Math 254: Student Learning Objectives

[NEW]

A closer look at the Cognitive Process Dimension 1. remember: recognize, recall

3. apply: execute, implement

5. evaluate: check, critique

2. understand: interpret, exemplify, classify, summarize, infer, compare, explain

4. analyze: differentiate, organize, attribute

6. create: generate, plan, produce

Introductory Math classes tend to aim at reaching “Level #3–4” in the Cognitive Process Dimension.

Peter Blomgren, [emailprotected]

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The Professor The Class — Overview The Class... Linear Algebra

Literature & Syllabus Student Learning Objectives Grading Expectations and Procedures

Math 254: Student Learning Objectives

[NEW]

A closer look at the Knowledge Dimension 1. factual knowledge of: terminology specific details and elements 2. conceptual knowledge of: classifications and categories principles and generalizations theories, models, and structures

3. procedural knowledge of: subject-specific skills and algorithms subject-specific techniques and methods criteria for determining when to use appropriate procedures 4. metacognitive strategic knowledge knowledge about cognitive tasks, including appropriate contextual and conditional knowledge self-knowledge

Introductory Math classes tend to aim at reaching “Level #3” in the Knowledge Dimension. Peter Blomgren, [emailprotected]

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Literature & Syllabus Student Learning Objectives Grading Expectations and Procedures

Math 254: Student Learning Objectives

[NEW]

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Figure: Now, if we think of the learning process in terms of moving upward from (1,1) = (memorize,facts) to higher levels; such as (3,3) = (perform,Gram-Schmidt Process); we can formulate more useful Student Learning Objectives. Peter Blomgren, [emailprotected]

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The Professor The Class — Overview The Class... Linear Algebra

Literature & Syllabus Student Learning Objectives Grading Expectations and Procedures

Math 254: Student Learning Objectives

[NEW]

At the end of the semester you should be able to... (1,1) Know basic definitions of Scalars ∈ R, Vectors ∈ Rn , and Matrices ∈ Rm×n (n,m) ..... [additional steps] ..... (2,2) Understand the Geometry of Linear Transformations (2,2) Understand the concepts of Subspaces, Bases, and Linear Independence (3,3) Perform an Orthogonal Projection onto a Vector Subspace (3,3) Perform the Gram-Schmidt Process on a Matrix A, and identify the resulting Q-R decomposition (3,3) Compute the Eigenvalues and Eigenvectors of a Matrix A

Peter Blomgren, [emailprotected]

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The Professor The Class — Overview The Class... Linear Algebra

Literature & Syllabus Student Learning Objectives Grading Expectations and Procedures

Math 254: Introduction — Grading etc.

10% i>Clicker in-class mini-quizzes 20% Homework (Online, collected via WeBWorK), ≈8 assignments 15% Midterm #1 15% Midterm #2 15% Midterm #3 25% Final

Peter Blomgren, [emailprotected]

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The Professor The Class — Overview The Class... Linear Algebra

Literature & Syllabus Student Learning Objectives Grading Expectations and Procedures

Expectations and Procedures, I

Class attendance is (α) HIGHLY RECOMMENDED — Homework and announcements will be posted on the class web page; or (β) MANDATORY for ALL in-class presentations. If/when you attend class: Please be on time. Please pay attention. Please turn off mobile phones. Please be courteous to other students and the instructor. Abide by university statutes, and all applicable local, state, and federal laws.

Peter Blomgren, [emailprotected]

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The Professor The Class — Overview The Class... Linear Algebra

Literature & Syllabus Student Learning Objectives Grading Expectations and Procedures

Expectations and Procedures, II Please, turn in assignments on time. (The instructor reserves the right not to accept late assignments.) The instructor will make special arrangements for students with documented learning disabilities and will try to make accommodations for other unforeseen circ*mstances, e.g. illness, personal/family crises, etc. in a way that is fair to all students enrolled in the class. Please contact the instructor EARLY regarding special circ*mstances. Students are expected and encouraged to ask questions in class! Students are expected and encouraged to to make use of office hours! If you cannot make it to the scheduled office hours: contact the instructor to schedule an appointment! Peter Blomgren, [emailprotected]

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The Professor The Class — Overview The Class... Linear Algebra

Literature & Syllabus Student Learning Objectives Grading Expectations and Procedures

Expectations and Procedures, III Missed midterm exams: Don’t miss exams! The instructor reserves the right to schedule make-up exams, make such exams oral presentation, and/or base the grade solely on other work (including the final exam). Missed final exam/presentation: Don’t miss the final! Contact the instructor ASAP or a grade of WU or F will be assigned. Academic honesty: submit your own work — but feel free to discuss homework with other students in the class! It’s OK to ask “Uncle Google” and “Aunt Wiki” for help and ideas, but process the information and make it your own, AND cite any and all sources (outside of class material) you use. Peter Blomgren, [emailprotected]

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Literature & Syllabus Student Learning Objectives Grading Expectations and Procedures

Honesty Pledges, I

The following Honesty Pledge must be included in all programs you submit (as part of homework and/or projects): I, (your name), pledge that this program is completely my own work, and that I did not take, borrow or steal code from any other person, and that I did not allow any other person to use, have, borrow or steal portions of my code. I understand that if I violate this honesty pledge, I am subject to disciplinary action pursuant to the appropriate sections of the San Diego State University Policies.

Work missing the honesty pledge may not be graded!

Peter Blomgren, [emailprotected]

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The Professor The Class — Overview The Class... Linear Algebra

Literature & Syllabus Student Learning Objectives Grading Expectations and Procedures

Honesty Pledges, II

Larger reports must contain the following text: I, (your name), pledge that this report is completely my own work, and that I did not take, borrow or steal any portions from any other person. Any and all references I used are clearly cited in the text. I understand that if I violate this honesty pledge, I am subject to disciplinary action pursuant to the appropriate sections of the San Diego State University Policies. Your signature.

Work missing the honesty pledge may not be graded!

Peter Blomgren, [emailprotected]

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The Professor The Class — Overview The Class... Linear Algebra

Resources Formal Prerequisites Course Technology and Resources

Math 254: Computer Resources Some in-class demonstrations will utilize MATLAB, but this class does NOT (yet) require any programming. IF you want to “play” with MATLAB: — You will need access to a computing environment in which to write your code. You can use the Rohan Sun Enterprise system or another capable system. [http://www-rohan.sdsu.edu/raccts.html] You may also want to consider buying the student version of Matlab: http://www.mathworks.com/ But why would you?!? — SDSU students can download a copy of matlab from http://www-rohan.sdsu.edu/∼download/matlab.html [Licensing Subject to Change With Minimal Notice]

Peter Blomgren, [emailprotected]

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The Professor The Class — Overview The Class... Linear Algebra

Resources Formal Prerequisites Course Technology and Resources

Math 254: Introduction — What you should know already

Math 151 (with a minimum grade of C∗ ) 151 ⇒ Calculus II (requires Math 150 with minimum grade of C) • Techniques and applications of integration. Improper integrals. Differential equations. Infinite series. Conic sections. Curves in parametric form, polar coordinates. 150 ⇒ Calculus I • Algebraic and transcendental functions. Continuity and limits. The derivative and its applications. The integral and the fundamental theorem of calculus.

Peter Blomgren, [emailprotected]

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The Professor The Class — Overview The Class... Linear Algebra

Resources Formal Prerequisites Course Technology and Resources

Course Technology Terminus.SDSU.EDU

lecture notes announcements schedule learning glass videos (you will like these!) Webwork.SDSU.EDU

homework Blackboard.SDSU.EDU

doing the right stuff (DRS) measures mediasite lecture capture (rewind the lecture!) gradebook Supplemental Instruction (SI) Hours i>Clickers: real time student engagement / mini-quizzes lecture + office hours (Prof/TA) Math Learning Center Peter Blomgren, [emailprotected]

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The Professor The Class — Overview The Class... Linear Algebra

The What? Why? and How?

Math 254: Introduction — What? Why? and How?

Let’s take a step back, and ask...

What is Mathematics?

Peter Blomgren, [emailprotected]

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The Professor The Class — Overview The Class... Linear Algebra

The What? Why? and How?

“The Google” has an Opinion...

Peter Blomgren, [emailprotected]

...do you?!

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The Professor The Class — Overview The Class... Linear Algebra

The What? Why? and How?

It’s Definitely Not a Spectator Sport Quote “Mathematics is not a spectator sport.” — Prof. Stanley Osher (UCLA)

... or more rudely stated:

Peter Blomgren, [emailprotected]

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The Professor The Class — Overview The Class... Linear Algebra

The What? Why? and How?

So How Do You Succeed in this Class? Actively participate by engaging with the material Pay attention for more than 12.93% of the lecture(s) Read Think Do problems Get stuck (figure out what you don’t know!) Think some more If still stuck, get help! Professor TA SI Sessions “Uncle” Google & “Aunt” Wiki Friends & Enemies

Curse the professor (it helps!) repeat

Emotional Engagement!

Also: http://terminus.sdsu.edu/SDSU/Math254/?r=success Peter Blomgren, [emailprotected]

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The Professor The Class — Overview The Class... Linear Algebra

Peter Blomgren, [emailprotected]

The What? Why? and How?

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