blubird

Bryan Lu's LaTeX Package (and other stuff)

Instructions for Use

For making handouts: download blubase.sty and blubird.sty. Use class scrartcl in your document and include \usepackage{blubird} in your preamble.

For writing up problem sets: download blubase.sty, problemset.cls. Use document class problemset, and include \studname{<your name>}, \studmail{<your email>}, \coursename{<course name>}, \duedate{<the date>}, and \hwNo{<problem set #>} in the preamble. The template ps-template.tex is recommended as it automatically fills in these fields.

Summary of Contents

Note: A lot of this package reimplements the functionality of the physics package in LaTeX. I've been told that package sucks so I've included most of those macros explicitly and extended them to be more flexible.

This is not meant to be a complete listing; but the following describes at a high level what kinds of commands are included in this package:

BIG NOTE: Redefinition of \bf: You shouldn't be using this anyway for good-practice reasons, so I've repurposed it to be the shorthand for \mathbf.

Sets of Numbers

All common sets of numbers (the naturals, integers, rationals, reals, complex, etc.) have macros. For example, the integers are \ZZ. The set of n x m matrices also now has a shortcut - Mat(n, m) can be written as \mat(n, m).

Complex Number Operators

Real and imaginary part operators don't look super ugly, capitalized for principal-valued functions for Log and Arg.

Combinatorics

Implemented from my Concrete Math (Spring 2019) class. Lots of commands dedicated to Knuth's Stirling number notation (for both the first and second kinds).

Functions, Calculus and Calculus Operators

Lots of commands to abbreviate derivatives, partial derivatives, and mixed partials. Has vector operators for the gradient, curl, divergence, and Laplacian. Added some hyperbolic functions and inverses of some specific trig/hyperbolic trig functions not already covered.

Physics Shenanigans

Has stuff for the Lagrangian and Hamiltonian and other things in the cool, swirly mathcal font.

Dirac Notation and Commutators

Supports all that jazz, from my (incomplete) transcription of my Quantum/Electrodynamics (2018-2019) class notes.

MATH 2230/40 Notation

Any other notation that's not the above stuff that appears in Hubbard (5th ed.) is here. Some notes:

• Chapter 0/Other:
  • I prefer \varepsilon to \epsilon, so the former is abbreviated as \eps.
• Chapter 1:
  • The Jacobian and derivative of a function as in 1.7 are automatically in brackets to indicate they are matrices. Uses mathcal font.
  • Interior, closure, and boundary symbols added.
  • Abbreviations for starting/ending matrices. Separate commands for inline matrices and display-style matrices.
• Chapter 2:
  • Augmented matrices (both parenthesis and bracket delimiters) added
  • span is now \spn, image is \im. (Hubbard's notation uses img for the image, I prefer im)
  • dimension is \dim, kernel is \ker, which are both implemented by default
  • added notation for change of basis matrix
  • "Divided matrices" (both parenthesis and bracket delimiters) when computing matrix inverses added
• Chapter 3:
  • the trace of a matrix finally implemented as \tr!
  • Taylor series notation added. First argument is the function f; the second, the order of the polynomial n; and the third, the center of the series \mathbf{a}.
  • because not even Hubbard can decide which way the indices go for the multi-exponents, I have made the executive decision to make \multexp{n}, the set of all multi-exponents in n variables, have the n as the subscript. If you don't like it, change it.
• Chapter 4:
  • indicator function \mathbf{1}, with argument for the region for which the function is 1.
  • the volume function \vol for the volume of various regions
  • the symbol for the set of dyadic pavings, \dpav, with one argument for the order N of the paving.
  • Made it easier to type absolute-value differential with \dvol
  • \sgn and \sign used for signature (of a permutation), or sign of a permutation (or really anything), use whichever you like
• Chapter 5:
  • \area macro for two dimensions
  • \hausd for Hausdorff dimension/measure notation as used by Professor Manning in lecture - not standard (read: not used by Hubbard in the book itself)
  • \dmanvol for typing out the big square root of determinants if you're feeling a little lazy, don't recommend using regularly
• Chapter 6:
  • \baset to represent the symbols used for an ordered basis of a vector space V (with the subscript V) or as "operating" on a manifold, giving ordered bases of the tangent space at every point on a smooth manifold
  • \extd for the exterior derivative of a form
  • \permset used in the definition of the wedge product (no special symbol other than standard amssymb one for wedges)

Abstract Algebra Notation

• \iso easier for writing isomorphisms
• \nsub for writing normal subgroups (may implement the other direction -- normal "supergroups"?)
• \aut for the automorphism group
• \inn for the inner automorphism group
• \out for the outer automorphism group
• \edom for the set of endomorphisms M -> M on an R-module (or vector space)
• \tor for the torsion set of an R-module
• \ann for the annihilator of an R-module