From f74458a6d8b557934be26ad37e8416d73699bf3a Mon Sep 17 00:00:00 2001 From: Jeremy Sylvestre Date: Wed, 11 Feb 2026 17:26:27 -0700 Subject: [PATCH] Update project: Sylvestre's DLA --- src/sylvestre-DLA.xml | 59 +++++++++++++++++++++++++++++++++++++++---- 1 file changed, 54 insertions(+), 5 deletions(-) diff --git a/src/sylvestre-DLA.xml b/src/sylvestre-DLA.xml index 43fd418..88a9519 100644 --- a/src/sylvestre-DLA.xml +++ b/src/sylvestre-DLA.xml @@ -19,9 +19,8 @@ interest to the individuals named above. - + Discover Linear Algebra - A First Course in Linear Algebra Jeremy Sylvestre U of Alberta (Augustana Campus) @@ -42,14 +41,63 @@ interest to the individuals named above. landing="https://sites.ualberta.ca/~jsylvest/books/dla.html" source="https://github.com/jjrsylvestre/dla" html="https://sites.ualberta.ca/~jsylvest/books/DLA/" + pdf="https://sites.ualberta.ca/~jsylvest/books/dla.html#book-links" + ancillary1="https://sites.ualberta.ca/~jsylvest/books/dla.html#resources" /> -

A discovery-based approach to linear algebra.

-

Extended material to cover a second course in linear algebra is being finalized and will be released Summer 2019.

+

+ The goal of this book is to help students learn about mathematics rather than try to teach them a bunch of mathematics. + Using the paradigm of guided-discovery, + students are led to model mathematics as a discipline and practice of thought and investigation, + rather than merely subject matter to absorb. + The beautiful topic of linear algebra is well-suited to this philosophy and pedagogical approach, + as many of its fundamental patterns are readily apparent from approachable examples. +

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+ One-semester version: + systems and matrices; + vectors and vector spaces; + eigenvalues/eigenvectors and diagonalization. +

+

+ Two-semester version: + material from the one-semester version with additional chapters on + complex matrices and spaces, and change of basis; + similarity and matrix forms; + inner product spaces; + linear transformations. + Also included are appendices on complex numbers and on performing typical calculations using + SageMath. +

+

+ Chapters are (mostly) consistently structured into the following sections to give the student a uniform flow to encountering each new collection of ideas and patterns: +

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  • Discovery guide: + Initial encounter through discovery- and problem-solving-based activities. +
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  • Terminology and notation: + Introduction of the communication tools necessary to begin a more sophisticated conversation about the new topics. +
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  • Concepts: + Fuller discussion of the new topics, grounded in reflections on the questions and results of the Discovery guide section. +
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  • Examples: + Computational examples to assist students with the procedural tasks related to the new topics, as well as additional examples that serve to illustrate certain concepts. +
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  • Theory: A more formal and general description of the concepts, with proofs.
    • +
+ In addition, + Exercises and Reflect on your understanding (reading questions) sections are currently being added. +

+

+ See the landing page + and the Preface + for more details on the pedagogical choices made in this book. +

- Textbook for a discovery-based approach to linear algebra. + A discovery-based approach to linear algebra.