$$\newcommand{\id}{\mathrm{id}}$$ $$\newcommand{\Span}{\mathrm{span}}$$ $$\newcommand{\kernel}{\mathrm{null}\,}$$ $$\newcommand{\range}{\mathrm{range}\,}$$ $$\newcommand{\RealPart}{\mathrm{Re}}$$ $$\newcommand{\ImaginaryPart}{\mathrm{Im}}$$ $$\newcommand{\Argument}{\mathrm{Arg}}$$ $$\newcommand{\norm}[1]{\| #1 \|}$$ $$\newcommand{\inner}[2]{\langle #1, #2 \rangle}$$ $$\newcommand{\Span}{\mathrm{span}}$$

# Acknowledgements

$$\newcommand{\vecs}[1]{\overset { \scriptstyle \rightharpoonup} {\mathbf{#1}} }$$ $$\newcommand{\vecd}[1]{\overset{-\!-\!\rightharpoonup}{\vphantom{a}\smash {#1}}}$$$$\newcommand{\id}{\mathrm{id}}$$ $$\newcommand{\Span}{\mathrm{span}}$$ $$\newcommand{\kernel}{\mathrm{null}\,}$$ $$\newcommand{\range}{\mathrm{range}\,}$$ $$\newcommand{\RealPart}{\mathrm{Re}}$$ $$\newcommand{\ImaginaryPart}{\mathrm{Im}}$$ $$\newcommand{\Argument}{\mathrm{Arg}}$$ $$\newcommand{\norm}[1]{\| #1 \|}$$ $$\newcommand{\inner}[2]{\langle #1, #2 \rangle}$$ $$\newcommand{\Span}{\mathrm{span}}$$ $$\newcommand{\id}{\mathrm{id}}$$ $$\newcommand{\Span}{\mathrm{span}}$$ $$\newcommand{\kernel}{\mathrm{null}\,}$$ $$\newcommand{\range}{\mathrm{range}\,}$$ $$\newcommand{\RealPart}{\mathrm{Re}}$$ $$\newcommand{\ImaginaryPart}{\mathrm{Im}}$$ $$\newcommand{\Argument}{\mathrm{Arg}}$$ $$\newcommand{\norm}[1]{\| #1 \|}$$ $$\newcommand{\inner}[2]{\langle #1, #2 \rangle}$$ $$\newcommand{\Span}{\mathrm{span}}$$

We would like to acknowledge the following instructors for their helpful comments and suggestions.

• Tibor Beke, UMass Lowell

• Alex DeCourcy, UMass Lowell

• Vince DiChiacchio

• Warren Grieff, UMass Lowell

• Matthew Haner, Mansfield University (PA)

• Dan Klain, UMass Lowell

• Sitansu Mittra, UMass Lowell

• Ravi Montenegro, UMass Lowell

• Tony Penta, UMass Lowell

• Jim Propp, UMass Lowell

• Thao Tran, UMass Lowell

• Richard Voss, Florida Atlantic U.

I'd like to particularly single out Jim Propp for his close scrutiny, along with that of his students, many of whom are listed below.

I would like to thank Rob Beezer, David Farmer, Karl-Dieter Crisman and other participants on the pretext-xml-support group for their guidance and work on MathBook XML, which has now been renamed PreTeXt. Thanks to the Pedagogy Subcommittee of the UMass Lowell Transformational Education Committee for their financial assistance in helping getting this project started.

Many students have provided feedback and pointed out typos in several editions of this book. They are listed below. Students with no affiliation listed are from UMass Lowell.

• Ryan Allen

• Rebecca Alves

• Anonymous student from Florida Atlantic U.

• Junaid Baig

• Anju Balaji

• Carlos Barrientos

• Chris Berns

• Raymond Berger, Eckerd College

• Brianne Bindas

• Nicholas Bishop

• Nathan Blood

• Cameron Bolduc

• Sam Bouchard

• Eric Breslau

• Rachel Bryan

• Courtney Caldwell

• Joseph Calles

• Rebecca Campbelli

• AJ Capone

• Eric Carey

• Emily Cashman

• Cora Casteel

• Rachel Chaiser, U. of Puget Sound

• Sam Chambers

• Vanessa Chen

• Hannah Chiodo

• Sofya Chow

• David Connolly

• Sean Cummings

• Alex DeCourcy

• Ryan Delosh

• Hillari Denny

• Matthew Edwards

• John El-Helou

• Josh Everett

• Christian Franco

• Anthony Gaeta

• Lisa Gieng

• Holly Goodreau

• Lilia Heimold

• Kevin Holmes

• Benjamin Houle

• Alexa Hyde

• Michael Ingemi

• Eunji Jang

• Kyle Joaquim

• Devin Johnson

• Jeremy Joubert

• William Jozefczyk

• Antony Kellermann

• Yorgo A. Kennos

• Thomas Kiley

• Cody Kingman

• Leant Seu Kim

• Jessica Kramer

• John Kuczynski

• Auris Kveraga

• Justin LaGree

• Daven Lagu

• Kendra Lansing

• Gregory Lawrence

• Pearl Laxague

• Kevin Le

• Matt LeBlanc

• Maxwell Leduc

• Ariel Leva

• Robert Liana

• Tammy Liu

• Laura Lucaciu

• Kelly Ly

• Kevin Mackie, Learning Assistant

• Alexandra Mai

• Andrew Magee

• Matthew Malone

• Logan Mann

• Sam Marquis

• Amy Mazzucotelli

• Nick McArdle

• Christine McCarthy

• Shelbylynn McCoy

• Conor McNierney

• Albara Mehene

• Joshua Michaud

• Max Mints

• Charles Mirabile

• Timothy Miskell

• Genevieve Moore

• Mike Morley

• Zach Mulcahy

• Tessa Munoz

• Zachary Murphy

• Carol Nguyen

• Hung Nguyen

• Shelly Noll

• Steven Oslan, the champion typo finder!

• Harsh Patel

• Beck Peterson

• Donna Petitti

• Paola Pevzner

• Samantha Poirier

• Roshan Ravi

• Ian Roberts

• John Raisbeck

• Derek Ross

• Tyler Ross

• Jacob Rothmel

• Zach Rush

• Steve Sadler, Bellevue College (WA)

• Doug Salvati

• Chita Sano

• Noah Schultz

• Anna Sergienko

• Ben Shipman

• Florens Shosho

• Lorraine Sill

• Jonathan Silva

• Joshua Simard

• Mason Sirois

• Sana Shaikh

• Joel Slebodnick

• Greg Smelkov

• Andrew Somerville

• Alicia Stransky

• Brandon Swanberg

• Joshua Sullivan

• James Tan

• Bunchhoung Tiv

• Joanel Vasquez

• Rolando Vera

• Anh Vo

• Nick Wackowski

• Ryan Wallace

• Uriah Wardlaw

• Zachary Watkins

• Steve Werren

• Laura Wikoff

• Henry Zhu

• Several students at Luzurne County Community College (PA)