diff --git a/_quarto-website.yml b/_quarto-website.yml index 914447684..407c01bd2 100644 --- a/_quarto-website.yml +++ b/_quarto-website.yml @@ -70,6 +70,10 @@ website: - algebra-exponentials.qmd - algebra-trigonometry.qmd - algebra-complex.qmd + - text: "Proof Writing" + href: proof-writing.qmd + - text: "Induction and Recursion" + href: induction.qmd - text: "Measures" menu: - text: "Overview" @@ -113,10 +117,6 @@ website: - optimization-newton.qmd - optimization-gradient-descent.qmd - optimization-quasi-newton.qmd - - text: "Proof Writing" - href: proof-writing.qmd - - text: "Induction and Recursion" - href: induction.qmd right: - icon: github href: https://github.com/Morrison-Lab/mds @@ -155,6 +155,8 @@ website: - algebra-exponentials.qmd - algebra-trigonometry.qmd - algebra-complex.qmd + - proof-writing.qmd + - induction.qmd - section: "Measures" href: measures.qmd contents: @@ -193,8 +195,6 @@ website: - optimization-newton.qmd - optimization-gradient-descent.qmd - optimization-quasi-newton.qmd - - proof-writing.qmd - - induction.qmd # Each type below gets a title bar (type, number, name) apart from the body, # and folds, open by default: the callouty-theorem defaults since 1.4.0. diff --git a/index.qmd b/index.qmd index 1b2b84c71..15a92d608 100644 --- a/index.qmd +++ b/index.qmd @@ -24,7 +24,14 @@ mathematical notation, algebra (including exponentials and logarithms), univariate calculus, linear algebra, vector calculus, optimization, and proof writing. Some key results are listed here, -organized by topic: +organized by topic. + +The first six topics are the foundations. +Apart from a few remarks in Algebra that touch on calculus, +they assume no calculus, +so a course on discrete math, +such as [Math for Computer Science](https://morrison-lab.github.io/mcs/), +can build on them directly: - [Notation](notation.qmd): common symbols @@ -46,6 +53,13 @@ organized by topic: - [Algebra](algebra.qmd): equalities and [inequalities](proof-writing.qmd#def-inequality), infimum and supremum, percent, sums, products, quotients, limits of sums, notational shorthands, exponentials and logarithms +- [Proof Writing](proof-writing.qmd): + propositions, quantifiers, proofs and derivations, and showing and annotating every step of a [derivation](proof-writing.qmd#def-derivation) +- [Induction and Recursion](induction.qmd): + [recursively defined sequences](induction.qmd#def-recursive-sequence) and [strong induction](induction.qmd#def-strong-induction) + +The remaining topics build on the foundations and on each other: + - [Measures](measures.qmd): $\sigma$-algebras, [finite](functions.qmd#def-finite-set) and [countable additivity](measures.qmd#def-countable-additivity), measures, and the counting measure @@ -65,8 +79,6 @@ organized by topic: - [Optimization](optimization.qmd): optimality conditions, Taylor approximations, convexity in several variables, Lagrange multipliers, Newton's method, and gradient descent -- [Proof Writing](proof-writing.qmd): - propositions, quantifiers, proofs and derivations, and showing and annotating every step of a [derivation](proof-writing.qmd#def-derivation) # Further reading {.unnumbered}