first day of notes

3 files changed, 458 insertions, 0 deletions

diff --git a/LICENSE b/LICENSE
new file mode 100644
index 0000000..8992429
--- /dev/null
+++ b/LICENSE
@@ -0,0 +1,354 @@
+Copyright 2020 (c) Holden Rohrer
+Attribution-ShareAlike 4.0 International
+
+=======================================================================
+
+Creative Commons Attribution-ShareAlike 4.0 International Public
+License
+
+By exercising the Licensed Rights (defined below), You accept and agree
+to be bound by the terms and conditions of this Creative Commons
+Attribution-ShareAlike 4.0 International Public License ("Public
+License"). To the extent this Public License may be interpreted as a
+contract, You are granted the Licensed Rights in consideration of Your
+acceptance of these terms and conditions, and the Licensor grants You
+such rights in consideration of benefits the Licensor receives from
+making the Licensed Material available under these terms and
+conditions.
+
+
+Section 1 -- Definitions.
+
+  a. Adapted Material means material subject to Copyright and Similar
+     Rights that is derived from or based upon the Licensed Material
+     and in which the Licensed Material is translated, altered,
+     arranged, transformed, or otherwise modified in a manner requiring
+     permission under the Copyright and Similar Rights held by the
+     Licensor. For purposes of this Public License, where the Licensed
+     Material is a musical work, performance, or sound recording,
+     Adapted Material is always produced where the Licensed Material is
+     synched in timed relation with a moving image.
+
+  b. Adapter's License means the license You apply to Your Copyright
+     and Similar Rights in Your contributions to Adapted Material in
+     accordance with the terms and conditions of this Public License.
+
+  c. BY-SA Compatible License means a license listed at
+     creativecommons.org/compatiblelicenses, approved by Creative
+     Commons as essentially the equivalent of this Public License.
+
+  d. Copyright and Similar Rights means copyright and/or similar rights
+     closely related to copyright including, without limitation,
+     performance, broadcast, sound recording, and Sui Generis Database
+     Rights, without regard to how the rights are labeled or
+     categorized. For purposes of this Public License, the rights
+     specified in Section 2(b)(1)-(2) are not Copyright and Similar
+     Rights.
+
+  e. Effective Technological Measures means those measures that, in the
+     absence of proper authority, may not be circumvented under laws
+     fulfilling obligations under Article 11 of the WIPO Copyright
+     Treaty adopted on December 20, 1996, and/or similar international
+     agreements.
+
+  f. Exceptions and Limitations means fair use, fair dealing, and/or
+     any other exception or limitation to Copyright and Similar Rights
+     that applies to Your use of the Licensed Material.
+
+  g. License Elements means the license attributes listed in the name
+     of a Creative Commons Public License. The License Elements of this
+     Public License are Attribution and ShareAlike.
+
+  h. Licensed Material means the artistic or literary work, database,
+     or other material to which the Licensor applied this Public
+     License.
+
+  i. Licensed Rights means the rights granted to You subject to the
+     terms and conditions of this Public License, which are limited to
+     all Copyright and Similar Rights that apply to Your use of the
+     Licensed Material and that the Licensor has authority to license.
+
+  j. Licensor means the individual(s) or entity(ies) granting rights
+     under this Public License.
+
+  k. Share means to provide material to the public by any means or
+     process that requires permission under the Licensed Rights, such
+     as reproduction, public display, public performance, distribution,
+     dissemination, communication, or importation, and to make material
+     available to the public including in ways that members of the
+     public may access the material from a place and at a time
+     individually chosen by them.
+
+  l. Sui Generis Database Rights means rights other than copyright
+     resulting from Directive 96/9/EC of the European Parliament and of
+     the Council of 11 March 1996 on the legal protection of databases,
+     as amended and/or succeeded, as well as other essentially
+     equivalent rights anywhere in the world.
+
+  m. You means the individual or entity exercising the Licensed Rights
+     under this Public License. Your has a corresponding meaning.
+
+
+Section 2 -- Scope.
+
+  a. License grant.
+
+       1. Subject to the terms and conditions of this Public License,
+          the Licensor hereby grants You a worldwide, royalty-free,
+          non-sublicensable, non-exclusive, irrevocable license to
+          exercise the Licensed Rights in the Licensed Material to:
+
+            a. reproduce and Share the Licensed Material, in whole or
+               in part; and
+
+            b. produce, reproduce, and Share Adapted Material.
+
+       2. Exceptions and Limitations. For the avoidance of doubt, where
+          Exceptions and Limitations apply to Your use, this Public
+          License does not apply, and You do not need to comply with
+          its terms and conditions.
+
+       3. Term. The term of this Public License is specified in Section
+          6(a).
+
+       4. Media and formats; technical modifications allowed. The
+          Licensor authorizes You to exercise the Licensed Rights in
+          all media and formats whether now known or hereafter created,
+          and to make technical modifications necessary to do so. The
+          Licensor waives and/or agrees not to assert any right or
+          authority to forbid You from making technical modifications
+          necessary to exercise the Licensed Rights, including
+          technical modifications necessary to circumvent Effective
+          Technological Measures. For purposes of this Public License,
+          simply making modifications authorized by this Section 2(a)
+          (4) never produces Adapted Material.
+
+       5. Downstream recipients.
+
+            a. Offer from the Licensor -- Licensed Material. Every
+               recipient of the Licensed Material automatically
+               receives an offer from the Licensor to exercise the
+               Licensed Rights under the terms and conditions of this
+               Public License.
+
+            b. Additional offer from the Licensor -- Adapted Material.
+               Every recipient of Adapted Material from You
+               automatically receives an offer from the Licensor to
+               exercise the Licensed Rights in the Adapted Material
+               under the conditions of the Adapter's License You apply.
+
+            c. No downstream restrictions. You may not offer or impose
+               any additional or different terms or conditions on, or
+               apply any Effective Technological Measures to, the
+               Licensed Material if doing so restricts exercise of the
+               Licensed Rights by any recipient of the Licensed
+               Material.
+
+       6. No endorsement. Nothing in this Public License constitutes or
+          may be construed as permission to assert or imply that You
+          are, or that Your use of the Licensed Material is, connected
+          with, or sponsored, endorsed, or granted official status by,
+          the Licensor or others designated to receive attribution as
+          provided in Section 3(a)(1)(A)(i).
+
+  b. Other rights.
+
+       1. Moral rights, such as the right of integrity, are not
+          licensed under this Public License, nor are publicity,
+          privacy, and/or other similar personality rights; however, to
+          the extent possible, the Licensor waives and/or agrees not to
+          assert any such rights held by the Licensor to the limited
+          extent necessary to allow You to exercise the Licensed
+          Rights, but not otherwise.
+
+       2. Patent and trademark rights are not licensed under this
+          Public License.
+
+       3. To the extent possible, the Licensor waives any right to
+          collect royalties from You for the exercise of the Licensed
+          Rights, whether directly or through a collecting society
+          under any voluntary or waivable statutory or compulsory
+          licensing scheme. In all other cases the Licensor expressly
+          reserves any right to collect such royalties.
+
+
+Section 3 -- License Conditions.
+
+Your exercise of the Licensed Rights is expressly made subject to the
+following conditions.
+
+  a. Attribution.
+
+       1. If You Share the Licensed Material (including in modified
+          form), You must:
+
+            a. retain the following if it is supplied by the Licensor
+               with the Licensed Material:
+
+                 i. identification of the creator(s) of the Licensed
+                    Material and any others designated to receive
+                    attribution, in any reasonable manner requested by
+                    the Licensor (including by pseudonym if
+                    designated);
+
+                ii. a copyright notice;
+
+               iii. a notice that refers to this Public License;
+
+                iv. a notice that refers to the disclaimer of
+                    warranties;
+
+                 v. a URI or hyperlink to the Licensed Material to the
+                    extent reasonably practicable;
+
+            b. indicate if You modified the Licensed Material and
+               retain an indication of any previous modifications; and
+
+            c. indicate the Licensed Material is licensed under this
+               Public License, and include the text of, or the URI or
+               hyperlink to, this Public License.
+
+       2. You may satisfy the conditions in Section 3(a)(1) in any
+          reasonable manner based on the medium, means, and context in
+          which You Share the Licensed Material. For example, it may be
+          reasonable to satisfy the conditions by providing a URI or
+          hyperlink to a resource that includes the required
+          information.
+
+       3. If requested by the Licensor, You must remove any of the
+          information required by Section 3(a)(1)(A) to the extent
+          reasonably practicable.
+
+  b. ShareAlike.
+
+     In addition to the conditions in Section 3(a), if You Share
+     Adapted Material You produce, the following conditions also apply.
+
+       1. The Adapter's License You apply must be a Creative Commons
+          license with the same License Elements, this version or
+          later, or a BY-SA Compatible License.
+
+       2. You must include the text of, or the URI or hyperlink to, the
+          Adapter's License You apply. You may satisfy this condition
+          in any reasonable manner based on the medium, means, and
+          context in which You Share Adapted Material.
+
+       3. You may not offer or impose any additional or different terms
+          or conditions on, or apply any Effective Technological
+          Measures to, Adapted Material that restrict exercise of the
+          rights granted under the Adapter's License You apply.
+
+
+Section 4 -- Sui Generis Database Rights.
+
+Where the Licensed Rights include Sui Generis Database Rights that
+apply to Your use of the Licensed Material:
+
+  a. for the avoidance of doubt, Section 2(a)(1) grants You the right
+     to extract, reuse, reproduce, and Share all or a substantial
+     portion of the contents of the database;
+
+  b. if You include all or a substantial portion of the database
+     contents in a database in which You have Sui Generis Database
+     Rights, then the database in which You have Sui Generis Database
+     Rights (but not its individual contents) is Adapted Material,
+
+     including for purposes of Section 3(b); and
+  c. You must comply with the conditions in Section 3(a) if You Share
+     all or a substantial portion of the contents of the database.
+
+For the avoidance of doubt, this Section 4 supplements and does not
+replace Your obligations under this Public License where the Licensed
+Rights include other Copyright and Similar Rights.
+
+
+Section 5 -- Disclaimer of Warranties and Limitation of Liability.
+
+  a. UNLESS OTHERWISE SEPARATELY UNDERTAKEN BY THE LICENSOR, TO THE
+     EXTENT POSSIBLE, THE LICENSOR OFFERS THE LICENSED MATERIAL AS-IS
+     AND AS-AVAILABLE, AND MAKES NO REPRESENTATIONS OR WARRANTIES OF
+     ANY KIND CONCERNING THE LICENSED MATERIAL, WHETHER EXPRESS,
+     IMPLIED, STATUTORY, OR OTHER. THIS INCLUDES, WITHOUT LIMITATION,
+     WARRANTIES OF TITLE, MERCHANTABILITY, FITNESS FOR A PARTICULAR
+     PURPOSE, NON-INFRINGEMENT, ABSENCE OF LATENT OR OTHER DEFECTS,
+     ACCURACY, OR THE PRESENCE OR ABSENCE OF ERRORS, WHETHER OR NOT
+     KNOWN OR DISCOVERABLE. WHERE DISCLAIMERS OF WARRANTIES ARE NOT
+     ALLOWED IN FULL OR IN PART, THIS DISCLAIMER MAY NOT APPLY TO YOU.
+
+  b. TO THE EXTENT POSSIBLE, IN NO EVENT WILL THE LICENSOR BE LIABLE
+     TO YOU ON ANY LEGAL THEORY (INCLUDING, WITHOUT LIMITATION,
+     NEGLIGENCE) OR OTHERWISE FOR ANY DIRECT, SPECIAL, INDIRECT,
+     INCIDENTAL, CONSEQUENTIAL, PUNITIVE, EXEMPLARY, OR OTHER LOSSES,
+     COSTS, EXPENSES, OR DAMAGES ARISING OUT OF THIS PUBLIC LICENSE OR
+     USE OF THE LICENSED MATERIAL, EVEN IF THE LICENSOR HAS BEEN
+     ADVISED OF THE POSSIBILITY OF SUCH LOSSES, COSTS, EXPENSES, OR
+     DAMAGES. WHERE A LIMITATION OF LIABILITY IS NOT ALLOWED IN FULL OR
+     IN PART, THIS LIMITATION MAY NOT APPLY TO YOU.
+
+  c. The disclaimer of warranties and limitation of liability provided
+     above shall be interpreted in a manner that, to the extent
+     possible, most closely approximates an absolute disclaimer and
+     waiver of all liability.
+
+
+Section 6 -- Term and Termination.
+
+  a. This Public License applies for the term of the Copyright and
+     Similar Rights licensed here. However, if You fail to comply with
+     this Public License, then Your rights under this Public License
+     terminate automatically.
+
+  b. Where Your right to use the Licensed Material has terminated under
+     Section 6(a), it reinstates:
+
+       1. automatically as of the date the violation is cured, provided
+          it is cured within 30 days of Your discovery of the
+          violation; or
+
+       2. upon express reinstatement by the Licensor.
+
+     For the avoidance of doubt, this Section 6(b) does not affect any
+     right the Licensor may have to seek remedies for Your violations
+     of this Public License.
+
+  c. For the avoidance of doubt, the Licensor may also offer the
+     Licensed Material under separate terms or conditions or stop
+     distributing the Licensed Material at any time; however, doing so
+     will not terminate this Public License.
+
+  d. Sections 1, 5, 6, 7, and 8 survive termination of this Public
+     License.
+
+
+Section 7 -- Other Terms and Conditions.
+
+  a. The Licensor shall not be bound by any additional or different
+     terms or conditions communicated by You unless expressly agreed.
+
+  b. Any arrangements, understandings, or agreements regarding the
+     Licensed Material not stated herein are separate from and
+     independent of the terms and conditions of this Public License.
+
+
+Section 8 -- Interpretation.
+
+  a. For the avoidance of doubt, this Public License does not, and
+     shall not be interpreted to, reduce, limit, restrict, or impose
+     conditions on any use of the Licensed Material that could lawfully
+     be made without permission under this Public License.
+
+  b. To the extent possible, if any provision of this Public License is
+     deemed unenforceable, it shall be automatically reformed to the
+     minimum extent necessary to make it enforceable. If the provision
+     cannot be reformed, it shall be severed from this Public License
+     without affecting the enforceability of the remaining terms and
+     conditions.
+
+  c. No term or condition of this Public License will be waived and no
+     failure to comply consented to unless expressly agreed to by the
+     Licensor.
+
+  d. Nothing in this Public License constitutes or may be interpreted
+     as a limitation upon, or waiver of, any privileges and immunities
+     that apply to the Licensor or You, including from the legal
+     processes of any jurisdiction or authority.
diff --git a/README b/README
new file mode 100644
index 0000000..a81c7b8
--- /dev/null
+++ b/README
@@ -0,0 +1,29 @@
+# Holden Rohrer's work for the 2021-22 school year
+
+## Professors
+
+- Wing Suet Li for MATH 3406: Second Course in Linear Algebra
+- Mary Hudachek-Buswell for CS 1332: Data Structures and Algorithms
+- Mayya Zhilova for MATH 4261: Math Statistics I
+- Martin M Jarrio for PHYS 2212: Intro Physics II
+
+## Structure
+
+The growth of this repository will be pretty organic, but as a general
+rule it will consist exclusively of ASCII plain-text files (preferably
+as a final format, but sometimes using TeX to generate pdfs with a
+Makefile). At the top level there will be a folder for each prof,
+labeled with their last name (i.e. `markley/`), all-caps files like
+README, LICENSE, and PROGRESS for what is mostly metadata, and possibly
+some TeX format files. Git commits' commit times will act as the record
+for when different events occur.
+
+## License
+
+I have chosen to release this writing under CC BY-SA 4.0.
+The full license is available in LICENSE.
+
+The license does not apply to images that are used in
+`hireme/final-pres.odp` (which are used under an exception to copyright)
+nor any PDF forms I have included (which are likely insufficiently
+original to warrant copyright protection).
diff --git a/li/01_intro b/li/01_intro
new file mode 100644
index 0000000..8e8e9af
--- /dev/null
+++ b/li/01_intro
@@ -0,0 +1,75 @@
+Solution of a system is the set of points/combinations of variables that
+satisfy an equation like 3x+2y=1.
+
+[3 2][x
+      y] = 1 is equivalent
+A := [3 2]
+X := [x y]^T
+b := 1
+AX = b
+
+Some systems like:
+x - 2y = 0
+x + y = 1
+x - y = 2
+have no solutions.
+This can be written as a a matrix too.
+Asking "does this system have a solution" is equivalent to asking:
+Can [0 1 2]^T be written as a linear combination/in span of [1 1 1]^T
+and [-2 1 -1]^T
+
+-----
+How to solve Ax = b where A is an mxn matrix, x is a nx1 matrix of free
+variables, and b is a mx1 matrix of constants.
+
+Ex.
+A = [ 3 1  0 4
+      0 1  2 5
+      0 0 -1 1 ]
+x = [ x1 x2 x3 x4 ]^T
+b = [ 0 1 2 ]
+
+Find the free variable, and then back-substitute
+x4 = t
+-x3 + x4 = 2 --> x3 = t - 2
+x2 + 2*x3 + 5*x4 = 1 --> x2 + 2*(t-2) + 5*t = 1 --> x2 = 5 - 7t
+3*x1 + x2 + x4 = 0 --> 3*x1 + 5 - 7t + t = 0 --> x1 = -5/3 + 2t
+
+Pivot element := first non-zero element in a matrix row AND everything
+below it is zero
+
+A matrix is in *row echelon* form iff pivot elements are to the left of
+all pivot elements in a lower row.
+    Therefore, all non-zero rows have a pivot but not every column.
+Note: column echelon form also exists.
+
+Generally, solving Ax = B can be done by solving
+CAx = Cb where C is an invertible mxm matrix.
+Single row operations used in Gaussian elimination are a subset of these
+operations.
+
+Ex.
+A = 3x4 matrix.
+Multiply 1/3 to first row: 1/3 R1 -> R1.
+C = 3x3 matrix.
+[ 1/3 0 0
+  0   1 0
+  0   0 1 ] * A
+C^{-1} =
+[ 3 0 0
+  0 1 0
+  0 0 1 ]
+
+Switch rows R2 and R3:
+C = [ 1 0 0
+      0 0 1
+      0 1 0 ]
+C = C^{-1}
+
+Add cR1 to R3:
+C = [ 1 0 0
+      0 1 0
+      c 0 1 ]
+C^{-1} = [ 1 0 0
+           0 1 0
+          -c 0 1 ]