diff --git a/project.ptx b/project.ptx index 7c8304883..ef83f2b81 100644 --- a/project.ptx +++ b/project.ptx @@ -142,6 +142,15 @@ output-filename="TBIL-Linear-Algebra-Slides.pdf" > + + + + diff --git a/publication/instructor.ptx b/publication/instructor.ptx index 5b7b12122..3fff61ff0 100644 --- a/publication/instructor.ptx +++ b/publication/instructor.ptx @@ -35,7 +35,7 @@ - + diff --git a/publication/preview.ptx b/publication/preview.ptx index 635ebba89..aab29c134 100644 --- a/publication/preview.ptx +++ b/publication/preview.ptx @@ -35,7 +35,7 @@ - + diff --git a/publication/publication-619.ptx b/publication/publication-619.ptx new file mode 100644 index 000000000..668ca9f32 --- /dev/null +++ b/publication/publication-619.ptx @@ -0,0 +1,127 @@ + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + papersize={7in,10in},margin=1in + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + diff --git a/publication/publication.ptx b/publication/publication.ptx index df4ae293b..1cdfc6402 100644 --- a/publication/publication.ptx +++ b/publication/publication.ptx @@ -35,7 +35,7 @@ - + diff --git a/source/common/authors/lewis.ptx b/source/common/authors/lewis.ptx index 86cd5eaff..e370f9ec0 100644 --- a/source/common/authors/lewis.ptx +++ b/source/common/authors/lewis.ptx @@ -1,5 +1,6 @@ Drew Lewis + Center for Grading Reform drew.lewis@gmail.com diff --git a/source/linear-algebra/source/01-LE/01.ptx b/source/linear-algebra/source/01-LE/01.ptx index 364992f41..c57f4e96f 100644 --- a/source/linear-algebra/source/01-LE/01.ptx +++ b/source/linear-algebra/source/01-LE/01.ptx @@ -1,6 +1,7 @@
- Linear Systems, Vector Equations, and Augmented Matrices (LE1) + Linear Systems, Vector Equations, and Augmented Matrices (LE1) + Linear Systems and Vector Equations
  • @@ -1016,7 +1017,7 @@ Augmented matrix:
  • For a,b, \in \mathbb{R}, a \sim b if an only if |a|=|b|.

- + Sample Problem and Solution

Sample problem . diff --git a/source/linear-algebra/source/01-LE/02.ptx b/source/linear-algebra/source/01-LE/02.ptx index c003daa65..2d16ffb70 100644 --- a/source/linear-algebra/source/01-LE/02.ptx +++ b/source/linear-algebra/source/01-LE/02.ptx @@ -1,6 +1,7 @@

- Row Reduction of Matrices (LE2) + Row Reduction of Matrices (LE2) + Row Reduction of Matrices
  • @@ -944,7 +945,7 @@ rref(A) - + Sample Problem and Solution

    Sample problem . diff --git a/source/linear-algebra/source/01-LE/03.ptx b/source/linear-algebra/source/01-LE/03.ptx index 81a1a10ff..5899d5d9f 100644 --- a/source/linear-algebra/source/01-LE/03.ptx +++ b/source/linear-algebra/source/01-LE/03.ptx @@ -1,6 +1,7 @@

    - Counting Solutions for Linear Systems (LE3) + Counting Solutions for Linear Systems (LE3) + Counting Solutions for Linear Systems
    • @@ -474,7 +475,7 @@ different solutions. We'll learn how to find such solution sets in - + Sample Problem and Solution

      Sample problem . diff --git a/source/linear-algebra/source/01-LE/04.ptx b/source/linear-algebra/source/01-LE/04.ptx index d929411d3..7af85e7b3 100644 --- a/source/linear-algebra/source/01-LE/04.ptx +++ b/source/linear-algebra/source/01-LE/04.ptx @@ -1,6 +1,7 @@

      - Linear Systems with Infinitely-Many Solutions (LE4) + Linear Systems with Infinitely Many Solutions (LE4) + Linear Systems with Infinitely Many Solutions
      • @@ -437,7 +438,7 @@ Explain how to describe this solution set using set notation.
      • Suppose that a linear system has five equations and three unknowns and that the coefficient matrix has a pivot in every column. Then the linear system is consistent and has a unique solution.

      - + Sample Problem and Solution

      Sample problem . diff --git a/source/linear-algebra/source/01-LE/main.ptx b/source/linear-algebra/source/01-LE/main.ptx index 08e295caa..c36034be5 100644 --- a/source/linear-algebra/source/01-LE/main.ptx +++ b/source/linear-algebra/source/01-LE/main.ptx @@ -1,6 +1,7 @@ - Systems of Linear Equations (LE) + Systems of Linear Equations (LE) + Systems of Linear Equations diff --git a/source/linear-algebra/source/02-EV/01.ptx b/source/linear-algebra/source/02-EV/01.ptx index f470533c1..cbcd8876b 100644 --- a/source/linear-algebra/source/02-EV/01.ptx +++ b/source/linear-algebra/source/02-EV/01.ptx @@ -1,6 +1,7 @@

      - Linear Combinations (EV1) + Linear Combinations (EV1) + Linear Combinations
      • @@ -579,7 +580,7 @@ We can do this in a few parts. I've used bullets here to indicate all that needs - + Sample Problem and Solution

        Sample problem . diff --git a/source/linear-algebra/source/02-EV/02.ptx b/source/linear-algebra/source/02-EV/02.ptx index 09eb13de3..1c9c865b4 100644 --- a/source/linear-algebra/source/02-EV/02.ptx +++ b/source/linear-algebra/source/02-EV/02.ptx @@ -1,6 +1,7 @@

        - Spanning Sets (EV2) + Spanning Sets (EV2) + Spanning Sets
        • @@ -556,7 +557,7 @@ Given no additional information about the vectors \vec{v}_1,\dots, \vec{v}_m<

          - + Sample Problem and Solution

          Sample problem . diff --git a/source/linear-algebra/source/02-EV/03.ptx b/source/linear-algebra/source/02-EV/03.ptx index dc45ca331..6b74848a8 100644 --- a/source/linear-algebra/source/02-EV/03.ptx +++ b/source/linear-algebra/source/02-EV/03.ptx @@ -1,6 +1,7 @@

          - Subspaces (EV3) + Subspaces (EV3) + Subspaces
          • @@ -1113,7 +1114,7 @@ Is it possible that there is a subset of V containing fewer vectors than

            - + Sample Problem and Solution

            Sample problem . diff --git a/source/linear-algebra/source/02-EV/04.ptx b/source/linear-algebra/source/02-EV/04.ptx index c38203bf3..a9d3da439 100644 --- a/source/linear-algebra/source/02-EV/04.ptx +++ b/source/linear-algebra/source/02-EV/04.ptx @@ -1,6 +1,7 @@

            - Linear Independence (EV4) + Linear Independence (EV4) + Linear Independence
            • @@ -651,7 +652,7 @@ vectors that can form a linearly independent set? - + Sample Problem and Solution

              Sample problem . diff --git a/source/linear-algebra/source/02-EV/05.ptx b/source/linear-algebra/source/02-EV/05.ptx index 8604e89d3..3b7f2c64f 100644 --- a/source/linear-algebra/source/02-EV/05.ptx +++ b/source/linear-algebra/source/02-EV/05.ptx @@ -1,6 +1,7 @@

              - Identifying a Basis (EV5) + Identifying a Basis (EV5) + Identifying a Basis
              • @@ -599,7 +600,7 @@ Must a basis for the space P_2, the space of all quadratic polynomials, c - + Sample Problem and Solution

                Sample problem . diff --git a/source/linear-algebra/source/02-EV/06.ptx b/source/linear-algebra/source/02-EV/06.ptx index 9a9c2d06d..127f76e94 100644 --- a/source/linear-algebra/source/02-EV/06.ptx +++ b/source/linear-algebra/source/02-EV/06.ptx @@ -1,6 +1,7 @@

                - Subspace Basis and Dimension (EV6) + Subspace Basis and Dimension (EV6) + Subspace Basis and Dimension
                • @@ -477,7 +478,7 @@ Thus the basis for a subspace is not unique in general.

                  - + Sample Problem and Solution

                  Sample problem . diff --git a/source/linear-algebra/source/02-EV/07.ptx b/source/linear-algebra/source/02-EV/07.ptx index b88e7d610..bfe387632 100644 --- a/source/linear-algebra/source/02-EV/07.ptx +++ b/source/linear-algebra/source/02-EV/07.ptx @@ -1,6 +1,7 @@

                  - Homogeneous Linear Systems (EV7) + Homogeneous Linear Systems (EV7) + Homogeneous Linear Systems
                  • @@ -457,7 +458,7 @@ Prove that, for any column vector \vec{b} = \left[\begin{array}{c}b_1\\b_2\\

                    - + Sample Problem and Solution

                    Sample problem . diff --git a/source/linear-algebra/source/02-EV/main.ptx b/source/linear-algebra/source/02-EV/main.ptx index c730df712..a69c1329d 100644 --- a/source/linear-algebra/source/02-EV/main.ptx +++ b/source/linear-algebra/source/02-EV/main.ptx @@ -1,6 +1,7 @@ - Euclidean Vectors (EV) + Euclidean Vectors (EV) + Euclidean Vectors diff --git a/source/linear-algebra/source/03-AT/01.ptx b/source/linear-algebra/source/03-AT/01.ptx index 90eaf54e9..55c1f0e69 100644 --- a/source/linear-algebra/source/03-AT/01.ptx +++ b/source/linear-algebra/source/03-AT/01.ptx @@ -1,6 +1,7 @@

                    - Linear Transformations (AT1) + Linear Transformations (AT1) + Linear Transformations
                    • @@ -787,7 +788,7 @@ and T(cf(x))=cT(f(x)). - + Sample Problem and Solution

                      Sample problem . diff --git a/source/linear-algebra/source/03-AT/02.ptx b/source/linear-algebra/source/03-AT/02.ptx index ff6671ac5..55e2fe2f3 100644 --- a/source/linear-algebra/source/03-AT/02.ptx +++ b/source/linear-algebra/source/03-AT/02.ptx @@ -1,6 +1,7 @@

                      - Standard Matrices (AT2) + Standard Matrices (AT2) + Standard Matrices
                      • @@ -582,7 +583,7 @@ Prove that each transformation is linear, and that your matrix representations a

                        - + Sample Problem and Solution

                        Sample problem . diff --git a/source/linear-algebra/source/03-AT/03.ptx b/source/linear-algebra/source/03-AT/03.ptx index 214afe9e1..9e6da5a1d 100644 --- a/source/linear-algebra/source/03-AT/03.ptx +++ b/source/linear-algebra/source/03-AT/03.ptx @@ -1,6 +1,7 @@

                        - Image and Kernel (AT3) + Image and Kernel (AT3) + Image and Kernel
                        • @@ -816,7 +817,7 @@ Let \{\vec{v_1},\vec{v_2},\ldots,\vec{v_n}\} be a set of vectors in V<

                          - + Sample Problem and Solution

                          Sample problem . diff --git a/source/linear-algebra/source/03-AT/04.ptx b/source/linear-algebra/source/03-AT/04.ptx index 356e3d983..33609a6ff 100644 --- a/source/linear-algebra/source/03-AT/04.ptx +++ b/source/linear-algebra/source/03-AT/04.ptx @@ -1,6 +1,7 @@

                          - Injective and Surjective Linear Maps (AT4) + Injective and Surjective Linear Maps (AT4) + Injective and Surjective Linear Maps
                          • @@ -1117,7 +1118,7 @@ Prove that V is isomorphic toV^*. Here are some things to think ab

                          - + Sample Problem and Solution

                          Sample problem . diff --git a/source/linear-algebra/source/03-AT/05.ptx b/source/linear-algebra/source/03-AT/05.ptx index a6c5f85e9..30afa27dd 100644 --- a/source/linear-algebra/source/03-AT/05.ptx +++ b/source/linear-algebra/source/03-AT/05.ptx @@ -1,6 +1,7 @@

                          - Vector Spaces (AT5) + Vector Spaces (AT5) + Vector Spaces
                          • @@ -738,7 +739,7 @@ for all c\in \IR,\, (x_1,y_1),(x_2,y_2) \in V.

                            Consider the vector space of polynomials, \P_n. Suppose further that n= ab, where a \mbox{ and } b are each positive integers. Conjecture a relationship between M_{a,b} and \P_n. We will investigate this further in section

                            - + Sample Problem and Solution

                            Sample problem . diff --git a/source/linear-algebra/source/03-AT/06.ptx b/source/linear-algebra/source/03-AT/06.ptx index 3489fbcb6..305521f3e 100644 --- a/source/linear-algebra/source/03-AT/06.ptx +++ b/source/linear-algebra/source/03-AT/06.ptx @@ -1,6 +1,7 @@

                            - Polynomial and Matrix Spaces (AT6) + Polynomial and Matrix Spaces (AT6) + Polynomial and Matrix Spaces
                            • @@ -584,7 +585,7 @@ If you are given the values of a,b, and c, what value of d - + Sample Problem and Solution

                              Sample problem . diff --git a/source/linear-algebra/source/03-AT/main.ptx b/source/linear-algebra/source/03-AT/main.ptx index a7c32f70f..0e4434ae3 100644 --- a/source/linear-algebra/source/03-AT/main.ptx +++ b/source/linear-algebra/source/03-AT/main.ptx @@ -1,6 +1,7 @@ - Algebraic Properties of Linear Maps (AT) + Algebraic Properties of Linear Maps (AT) + Algebraic Properties of Linear Maps diff --git a/source/linear-algebra/source/04-MX/01.ptx b/source/linear-algebra/source/04-MX/01.ptx index 1a410101e..1f3f844e8 100644 --- a/source/linear-algebra/source/04-MX/01.ptx +++ b/source/linear-algebra/source/04-MX/01.ptx @@ -1,6 +1,7 @@

                              - Matrices and Multiplication (MX1) + Matrices and Multiplication (MX1) + Matrices and Multiplication
                              • @@ -392,7 +393,7 @@ Use the included map in this problem. - + Sample Problem and Solution

                                Sample problem . diff --git a/source/linear-algebra/source/04-MX/02.ptx b/source/linear-algebra/source/04-MX/02.ptx index b7a08c652..f4e6f9d78 100644 --- a/source/linear-algebra/source/04-MX/02.ptx +++ b/source/linear-algebra/source/04-MX/02.ptx @@ -1,6 +1,7 @@

                                - The Inverse of a Matrix (MX2) + The Inverse of a Matrix (MX2) + The Inverse of a Matrix
                                • @@ -545,7 +546,7 @@ Is the matrix \left[\begin{array}{ccc} 2 & 3 & 1 \\ -1 & -4 & - + Sample Problem and Solution

                                  Sample problem . diff --git a/source/linear-algebra/source/04-MX/03.ptx b/source/linear-algebra/source/04-MX/03.ptx index e1547f6f1..fd5114554 100644 --- a/source/linear-algebra/source/04-MX/03.ptx +++ b/source/linear-algebra/source/04-MX/03.ptx @@ -1,6 +1,7 @@

                                  - Change of Basis (MX3) + Change of Basis (MX3) + Change of Basis
                                  • @@ -274,7 +275,7 @@ Video coming soon to - + Sample Problem and Solution

                                    Sample problem . diff --git a/source/linear-algebra/source/04-MX/04.ptx b/source/linear-algebra/source/04-MX/04.ptx index d1b2d5dda..d7314f6b5 100644 --- a/source/linear-algebra/source/04-MX/04.ptx +++ b/source/linear-algebra/source/04-MX/04.ptx @@ -1,6 +1,7 @@

                                    - Row Operations as Matrix Multiplication (MX4) + Row Operations as Matrix Multiplication (MX4) + Row Operations as Matrix Multiplication
                                    • @@ -402,7 +403,7 @@ If you and a teammate were to do this independently, would you necessarily come

                                      - + Sample Problem and Solution

                                      Sample problem . diff --git a/source/linear-algebra/source/04-MX/main.ptx b/source/linear-algebra/source/04-MX/main.ptx index 94a84e8b1..c22b2aedb 100644 --- a/source/linear-algebra/source/04-MX/main.ptx +++ b/source/linear-algebra/source/04-MX/main.ptx @@ -1,6 +1,7 @@ - Matrices (MX) + Matrices (MX) + Matrices diff --git a/source/linear-algebra/source/05-GT/01.ptx b/source/linear-algebra/source/05-GT/01.ptx index 495724031..ecba992c2 100644 --- a/source/linear-algebra/source/05-GT/01.ptx +++ b/source/linear-algebra/source/05-GT/01.ptx @@ -1,6 +1,7 @@

                                      - Row Operations and Determinants (GT1) + Row Operations and Determinants (GT1) + Row Operations and Determinants
                                      • @@ -1141,7 +1142,7 @@ Or we may use a formula: - + Sample Problem and Solution

                                        Sample problem . diff --git a/source/linear-algebra/source/05-GT/02.ptx b/source/linear-algebra/source/05-GT/02.ptx index 262436fe5..37bb4e602 100644 --- a/source/linear-algebra/source/05-GT/02.ptx +++ b/source/linear-algebra/source/05-GT/02.ptx @@ -1,6 +1,7 @@

                                        - Computing Determinants (GT2) + Computing Determinants (GT2) + Computing Determinants
                                        • @@ -493,7 +494,7 @@ Based on the previous activities, which technique is easier for computing determ - + Sample Problem and Solution

                                          Sample problem . diff --git a/source/linear-algebra/source/05-GT/03.ptx b/source/linear-algebra/source/05-GT/03.ptx index d761497ad..98e87c210 100644 --- a/source/linear-algebra/source/05-GT/03.ptx +++ b/source/linear-algebra/source/05-GT/03.ptx @@ -1,6 +1,7 @@

                                          - Eigenvalues and Characteristic Polynomials (GT3) + Eigenvalues and Characteristic Polynomials (GT3) + Eigenvalues and Characteristic Polynomials
                                          • @@ -416,7 +417,7 @@ Set this characteristic polynomial equal to zero and factor to determine the eig - + Sample Problem and Solution

                                            Sample problem . diff --git a/source/linear-algebra/source/05-GT/04.ptx b/source/linear-algebra/source/05-GT/04.ptx index ed6310d7c..d15ddb1bb 100644 --- a/source/linear-algebra/source/05-GT/04.ptx +++ b/source/linear-algebra/source/05-GT/04.ptx @@ -1,6 +1,7 @@

                                            - Eigenvectors and Eigenspaces (GT4) + Eigenvectors and Eigenspaces (GT4) + Eigenvectors and Eigenspaces
                                            • @@ -177,7 +178,7 @@ associated with the eigenvalue 2. - + Sample Problem and Solution

                                              Sample problem . diff --git a/source/linear-algebra/source/05-GT/main.ptx b/source/linear-algebra/source/05-GT/main.ptx index eaf246f20..ae61c984d 100644 --- a/source/linear-algebra/source/05-GT/main.ptx +++ b/source/linear-algebra/source/05-GT/main.ptx @@ -1,6 +1,7 @@ - Geometric Properties of Linear Maps (GT) + Geometric Properties of Linear Maps (GT) + Geometric Properties of Linear Maps diff --git a/source/linear-algebra/source/meta/backmatter.ptx b/source/linear-algebra/source/meta/backmatter.ptx index e46e86ed5..8b73c41fc 100644 --- a/source/linear-algebra/source/meta/backmatter.ptx +++ b/source/linear-algebra/source/meta/backmatter.ptx @@ -3,11 +3,8 @@ Back Matter - - Appendix - - - + + Index diff --git a/source/linear-algebra/source/meta/definitions.ptx b/source/linear-algebra/source/meta/definitions.ptx index 3211f6cd0..32dc9a6dd 100644 --- a/source/linear-algebra/source/meta/definitions.ptx +++ b/source/linear-algebra/source/meta/definitions.ptx @@ -1,5 +1,5 @@ -

                                              + Definitions -
                                              \ No newline at end of file + \ No newline at end of file diff --git a/source/linear-algebra/source/meta/sample-exercises.ptx b/source/linear-algebra/source/meta/sample-exercises.ptx index 3cda48a8b..3da12f60e 100644 --- a/source/linear-algebra/source/meta/sample-exercises.ptx +++ b/source/linear-algebra/source/meta/sample-exercises.ptx @@ -1,5 +1,5 @@ -
                                              + Sample Exercises with Solutions

                                              Here we model one exercise and solution for each learning objective. @@ -38,4 +38,4 @@ for a complete solution. -

                                              +