Tag: index to a series of posts

My Favorite One-Liners: Index

I’m doing something that I should have done a long time ago: collecting a series of posts into one single post. The links below show my series on my favorite one-liners.

Mathematical Wisecracks for Almost Any Occasion: Part 2,  Part 7, Part 8, Part 12, Part 21, Part 28, Part 29, Part 41, Part 46, Part 53, Part 60, Part 63, Part 65, Part 71, Part 79, Part 84, Part 85, Part 100, Part 101,  Part 108, Part 109, Part 114, Part 118, Part 121

All-Purpose Anecdotes: Part 38, Part 50, Part 64, Part 70, Part 92, Part 94

Addressing Misconceptions: Part 3, Part 4, Part 11, Part 14, Part 15, Part 18, Part 30, Part 32, Part 33, Part 37, Part 45, Part 59

Tricky Steps in a Calculation: Part 5, Part 6

Greek alphabet and choice of variables: Part 40, Part 43, Part 56

Homework and exams: Part 39, Part 47, Part 55, Part 57, Part 58, Part 66, Part 77, Part 78, Part 91, Part 96, Part 97, Part 107

Inequalities: Part 99

Simplification: Part 10, Part 102, Part 103

Polynomials: Part 19, Part 48, Part 49, Part 81, Part 90

Inverses: Part 16

Exponential and Logarithmic Functions: Part 1, Part 42, Part 68, Part 80, Part 110

Trigonometry: Part 9, Part 69, Part 76, Part 106, Part 120

Complex numbers: Part 54, Part 67, Part 86, Part 112, Part 113

Sequences and Series: Part 20, Part 35, Part 111

Combinatorics: Part 27

Statistics: Part 22, Part 23, Part 36, Part 51, Part 52, Part 61, Part 95, Part 116

Probability: Part 26, Part 31, Part 62, Part 93, Part 122

Calculus: Part 24, Part 25, Part 72, Part 73, Part 74, Part 75, Part 83, Part 87, Part 88, Part 104, Part 115, Part 117

Logic and Proofs: Part 13, Part 17, Part 34, Part 44, Part 89, Part 98, Part 119

Differential Equations: Part 82, Part 105

Confirming Einstein’s General Theory of Relativity with Calculus: Index

I’m doing something that I should have done a long time ago: collecting a series of posts into one single post. The links below show my series on general relativity and the precession of Mercury’s orbit.

Part 1: Introduction

Part 2: Precession, polar coordinates, and conic sections

  • Part 2a: Graphically exploring precession
  • Part 2b: Polar coordinates and ellipses
  • Part 2c: Polar coordinates, circles, and parabolas
  • Part 2d: Polar coordinates and hyperbolas

Part 3: Method of successive approximations

Part 4: Principles from physics

  • Part 4a: Angular momentum
  • Part 4b: Acceleration in polar coordinates
  • Part 4c: Newton’s Second Law and Newton’s Law of Gravitation

Part 5: Orbits under Newtonian mechanics

  • Part 5a: Confirmation of solution
  • Part 5b: Derivation with calculus
  • Part 5c: Derivation with differential equations and the method of undetermined coefficients
  • Part 5d: Derivation with differential equations and variation of parameters

Part 6: Orbits under general relativity

  • Part 6a: New differential equation under general relativity
  • Part 6b: Confirmation of solution
  • Part 6c: Derivation with variation of parameters
  • Parts 6d, 6e, 6f, 6g, 6h, 6i, 6j: Rationale for the method of undetermined coefficients
  • Part 6k: Derivation with undetermined coefficients

Part 7: Computing precession

Part 8: Second- and third-order solutions with the method of successive approximations

Part 9: Pedagogical thoughts

Earlier this year, I presented these ideas for the UNT Math Department’s Undergraduate Mathematics Colloquium Series. The video of my lecture is below.

My Mathematical Magic Show: Index

I’m doing something that I should have done a long time ago: collecting a series of posts into one single post. The links below show the mathematical magic show that I’ll perform from time to time.

Part 1: Introduction.

Part 2a, Part 2b, and Part 2c: The 1089 trick.

Part 3a, Part 3b, and Part 3c: A geometric magic trick.

Part 4a: Part 4b, Part 4c, and Part 4d: A trick using binary numbers.

Part 5a, Part 5b, Part 5c, and Part 5d: A trick using the rule for checking if a number is a multiple of 9.

Part 7: The Fitch-Cheney card trick, which is perhaps the slickest mathematical card trick ever devised.

Part 8a, Part 8b, and Part 8c: A trick using Pascal’s triangle.

Part 9: Mentally computing n given n^5 if 10 \le n \le 99.

Part 10: A mathematical optical illusion.

Part 11: The 27-card trick, which requires representing numbers in base 3.

Part 6: The Grand Finale.

And, for the sake of completeness, here’s a picture of me just before I performed an abbreviated version of this show for UNT’s Preview Day for high school students thinking about enrolling at my university.

magician

Predicate Logic and Popular Culture: Index

I’m doing something that I should have done a long time ago: collecting a series of posts into one single post. The following links comprised my series on using examples from popular culture to illustrate principles of predicate logic. My experiences teaching these ideas to my discrete mathematics students led to my recent publication (John Quintanilla, “Name That Tune: Teaching Predicate Logic with Popular Culture,” MAA Focus, Vol. 36, No. 4, pp. 27-28, August/September 2016).

Unlike other series that I’ve made, this series didn’t have a natural chronological order. So I’ll list these by concept illustrated from popular logic. The vast majority of these examples were suggested by my students.

green lineLogical and \land:

  • Part 1: “You Belong To Me,” by Taylor Swift
  • Part 21: “Do You Hear What I Hear,” covered by Whitney Houston
  • Part 31: The Godfather (1972)
  • Part 45: The Blues Brothers (1980)
  • Part 53: “What Does The Fox Say,” by Ylvis
  • Part 54: “Billie Jean,” by Michael Jackson
  • Part 98: “Call Me Maybe,” by Carly Rae Jepsen.
  • Part 137: “Pen Pineapple Apple Pen,” by Pikotaro.
  • Part 142: “Galway Girl,” by Ed Sheeran.
  • Part 183: A memorable line from Avengers: Age of Ultron.
  • Part 184: A memorable line from Star Wars Episode I: The Phantom Menace.
  • Part 197: “That’s Life,” by Frank Sinatra.
  • Part 209: A line from The Office.
  • Part 242: A line from The Fellowship of the Ring.
  • Part 249: “We Didn’t Start the Fire,” by Billy Joel.
  • Part 252: A line from The Two Towers.
  • Part 253: “I’m Gonna Miss Her,” by Brad Paisley.
  • Part 261: A line from Spiderman 2.

Logical or \lor:

  • Part 1: Shawshank Redemption (1994)

Logical negation \lnot:

  • Part 1: Richard Nixon
  • Part 32: “Satisfaction!”, by the Rolling Stones
  • Part 39: “We Are Never Ever Getting Back Together,” by Taylor Swift
  • Part 129: “Blue Ain’t Your Color,” by Keith Urban.
  • Part 143: “Ain’t Worth The Whiskey,” by Cole Swindell.
  • Part 247: A line from The Fellowship of the Ring.

Logical implication \Rightarrow:

  • Part 1: Field of Dreams (1989), and also “Roam,” by the B-52s
  • Part 2: “Word Crimes,” by Weird Al Yankovic
  • Part 7: “I’ll Be There For You,” by The Rembrandts (Theme Song from Friends)
  • Part 43: “Kiss,” by Prince
  • Part 50: “I’m Still A Guy,” by Brad Paisley
  • Part 76: “You’re Never Fully Dressed Without A Smile,” from Annie.
  • Part 109: “Dancing in the Dark,” by Bruce Springsteen.
  • Part 122: “Keep Yourself Alive,” by Queen.
  • Part 140: “It Don’t Mean A Thing If It Ain’t Got That Swing,” by Ella Fitzgerald.
  • Part 174: A famous line from Rocky IV.
  • Part 176: A famous line from Game of Thrones.
  • Part 185: A line from Westworld.
  • Part 188: A line from Talladega Nights.
  • Part 195: “If We Were a Movie,” from the Hannah Montana series.
  • Part 207: A line from Name of the Wind, by Patrick Rothfuss.
  • Part 222: A line from The Notebook.
  • Part 234: “Battle Symphony,” by Linkin Park.
  • Part 235: A line from Suits.
  • Part 259: “Out There,” from “The Hunchback of Notre Dame.”
  • Part 269: “Dear Theodosia,” from Hamilton.

For all \forall:

  • Part 3: Casablanca (1942)
  • Part 4: A Streetcar Named Desire (1951)
  • Part 34: “California Girls,” by The Beach Boys
  • Part 37: Fellowship of the Ring, by J. R. R. Tolkien
  • Part 49: “Buy Me A Boat,” by Chris Janson
  • Part 57: “Let It Go,” by Idina Menzel and from Frozen (2013)
  • Part 65: “Stars and Stripes Forever,” by John Philip Sousa.
  • Part 68: “Love Yourself,” by Justin Bieber.
  • Part 69: “I Will Always Love You,” by Dolly Parton (covered by Whitney Houston).
  • Part 74: “Faithfully,” by Journey.
  • Part 79: “We’re Not Gonna Take It Anymore,” by Twisted Sister.
  • Part 87: “Hungry Heart,” by Bruce Springsteen.
  • Part 99: “It’s the End of the World,” by R.E.M.
  • Part 100: “Hold the Line,” by Toto.
  • Part 101: “Break My Stride,” by Matthew Wilder.
  • Part 102: “Try Everything,” by Shakira.
  • Part 108: “BO$$,” by Fifth Harmony.
  • Part 113: “Sweet Caroline,” by Neil Diamond.
  • Part 114: “You Know Nothing, Jon Snow,” from Game of Thrones.
  • Part 118: “The Lazy Song,” by Bruno Mars.
  • Part 120: “Cold,” by Crossfade.
  • Part 123: “Always on My Mind,” by Willie Nelson.
  • Part 127: Motif from Hamilton.
  • Part 131: Abraham Lincoln’s Second Inaugural Address.
  • Part 132: A famous line from The Fellowship of the Ring.
  • Part 133: A famous line from Braveheart.
  • Part 136: “I Don’t Wanna Live Forever,” by ZAYN and Taylor Swift.
  • Part 138: “Bohemian Rhapsody,” by Queen.
  • Part 144: “The Anchor,” by Bastille.
  • Part 146: A line from the video game series “Fallout”
  • Part 147: “Nobody’s Perfect,” from the Hannah Montana series.
  • Part 150: “Roar,” by Katy Perry.
  • Part 167: “Look What You Made Me Do,” by Taylor Swift.
  • Part 180: “Bohemian Rhapsody,” by Queen.
  • Part 181: “We Don’t Talk Anymore,” by Charlie Puth and Selena Gomez.
  • Part 189: “Tengo Muchas Alas / I Have Many Wings,” by Mana.
  • Part 190: “Eastside,” by Benny Blanco, Halsey, and Khalid.
  • Part 191: “I’m a Mess,” by Bebe Rexha.
  • Part 193: “Forever and Ever, Amen,” by Randy Travis.
  • Part 202: “Everything Is Awesome!!!,” from The Lego Movie.
  • Part 204: “She’s Always A Woman,” by Billy Joel.
  • Part 208: A line by Naruto in Masashi Kishimoto’s anime.
  • Part 211: “Everyone Lies To Me,” by Knuckle Puck.
  • Part 214: “Aeroplane,” by Björk.
  • Part 216: “Hound Dog,” by Elvis Presley.
  • Part 227: One Fish, Two Fish, Red Fish, Blue Fish, by Dr. Seuss.
  • Part 230: “Be Alright,” by Dean Lewis.
  • Part 231: “Everyone Wants To Be A Cat,” from The Aristocats.
  • Part 232: “Behind Blue Eyes,” by Limp Bizkit.
  • Part 236: A line from Dirty Dancing.
  • Part 243: “Better,” by Khalid.
  • Part 246: “Unfaithful,” by Rihanna.
  • Part 260: A line from Ratatouille.
  • Part 263: A line from Shakespeare’s As You Like It.
  • Part 264: “Bet On It,” from High School Musical 2.
  • Part 271: A line from Pirates of the Caribbean: The Curse of the Black Pearl.
  • Part 273: “Gaston,” from Beauty and the Beast.

For all and implication:

  • Part 8 and Part 9: “What Makes You Beautiful,” by One Direction
  • Part 13: “Safety Dance,” by Men Without Hats
  • Part 16: The Fellowship of the Ring, by J. R. R. Tolkien
  • Part 24 : “The Chipmunk Song,” by The Chipmunks
  • Part 55: The Quiet Man (1952)
  • Part 62: “All My Exes Live In Texas,” by George Strait.
  • Part 70: “Wannabe,” by the Spice Girls.
  • Part 72: “You Shook Me All Night Long,” by AC/DC.
  • Part 81: “Ascot Gavotte,” from My Fair Lady
  • Part 82: “Sharp Dressed Man,” by ZZ Top.
  • Part 86: “I Could Have Danced All Night,” from My Fair Lady.
  • Part 95: “Every Breath You Take,” by The Police.
  • Part 96: “Only the Lonely,” by Roy Orbison.
  • Part 97: “I Still Haven’t Found What I’m Looking For,” by U2.
  • Part 105: “Every Rose Has Its Thorn,” by Poison.
  • Part 107: “Party in the U.S.A.,” by Miley Cyrus.
  • Part 112: “Winners Aren’t Losers,” by Donald J. Trump and Jimmy Kimmel.
  • Part 115: “Every Time We Touch,” by Cascada.
  • Part 117: “Stronger,” by Kelly Clarkson.
  • Part 125: “Do Wot You Do,” by INXS.
  • Part 130: “Think of You,” by Chris Young and Cassadee Pope.
  • Part 135: “Can’t Feel My Face,” by The Weeknd.
  • Part 145: A line from Black Dynamite.
  • Part 152: “You Haven’t Done Nothin’,” by Stevie Wonder.
  • Part 155: “All The Lazy Boyfriends,” by They Might Be Giants.
  • Part 165: A famous quote by Eleanor Roosevelt.
  • Part 166: “Perfect,” by Ed Sheeran.
  • Part 172: “Twas the Night Before Christmas,” by Clement Clarke Moore.
  • Part 182: “How Far I’ll Go,” from Moana.
  • Part 192: A line from the videogame “Overwatch.”
  • Part 194: A line from the Dragon Ball franchise.
  • Part 196: “ME!,” by Taylor Swift.
  • Part 200: A line from the 1990s Spider-Man cartoons.
  • Part 201: “It’s Quiet Uptown,” from Hamilton.
  • Part 205: “Three Little Birds,” by Bob Marley.
  • Part 206: “Mudfootball,” by Jack Johnson.
  • Part 210: “On My Way,” by Alan Walker, Sabrina Carpenter, and Farruko.
  • Part 215: “Aging Rockers,” by Tim Hawkins.
  • Part 218: “Happy Together,” by The Turtles.
  • Part 223: “Too Deep to Turn Back,” by Daniel Caesar.
  • Part 224: “Nothing Gold Can Stay,” by Robert Frost.
  • Part 225: “He Stopped Loving Her Today,” by George Jones.
  • Part 229: A line from Mean Girls.
  • Part 233: “Emperor’s New Clothes,” by Panic! At The Disco.
  • Part 240: “For Those About To Rock (We Salute You),” by AC/DC.
  • Part 244: A famous line from Spiderman.
  • Part 248: The poem “All That Is Gold Does Not Glitter,” from The Fellowship of the Ring.
  • Part 251: “Survey Ladies,” from Animaniacs.
  • Part 265: “Every Time You Go Away,” by Paul Young.
  • Part 268: “Sweet Dreams,” by Eurhymics.
  • Part 270: A line from the anime “Naruto Shippuden.”
  • Part 272: “Be Our Guest,” from Beauty and the Beast.
  • Part 274: “He Stopped Loving Her Today,” by George Jones.

There exists \exists:

  • Part 10: “Unanswered Prayers,” by Garth Brooks
  • Part 15: “Stand by Your Man,” by Tammy Wynette (also from The Blues Brothers)
  • Part 36: Hamlet, by William Shakespeare
  • Part 57: “Let It Go,” by Idina Menzel and from Frozen (2013)
  • Part 93: “There’s No Business Like Show Business,” from Annie Get Your Gun (1946).
  • Part 94: “Not While I’m Around,” from Sweeney Todd (1979).
  • Part 104: “Wild Blue Yonder” (US Air Force)
  • Part 106: “No One,” by Alicia Keys.
  • Part 116: “Ocean Front Property,” by George Strait.
  • Part 139: “Someone in the Crowd,” from La La Land.
  • Part 149: “Someone Like You,” by Adele.
  • Part 151: “E-MO-TION,” by Carly Rae Jepsen.
  • Part 154: “I Wanna Dance With Somebody,” by Whitney Houston.
  • Part 162: “Think of You,” by Chris Young and Cassadee Pope.
  • Part 168: “Sorry,” by Halsey.
  • Part 175: “Someday We’ll Be Together,” by Diana Ross and the Supremes.
  • Part 177: “Try Everything,” by Shakira.
  • Part 186: “Someday,” by Nickelback.
  • Part 226: “The Wizard and I,” from Wicked.
  • Part 238: A line from the video game “Among Us.”
  • Part 250: “Ain’t No Mountain High Enough,” by Marvin Gaye.

Existence and uniqueness:

  • Part 14: “Girls Just Want To Have Fun,” by Cyndi Lauper
  • Part 20: “All I Want for Christmas Is You,” by Mariah Carey
  • Part 23: “All I Want for Christmas Is My Two Front Teeth,” covered by The Chipmunks
  • Part 29: “You’re The One That I Want,” from Grease
  • Part 30: “Only You,” by The Platters
  • Part 35: “Hound Dog,” by Elvis Presley
  • Part 73: “Dust In The Wind,” by Kansas.
  • Part 75: “Happy Together,” by The Turtles.
  • Part 77: “All She Wants To Do Is Dance,” by Don Henley.
  • Part 90: “All You Need Is Love,” by The Beatles.
  • Part 169: “Marry Me,” by Thomas Rhett.
  • Part 179: A line from “Harry Potter and the Sorcerer’s Stone.”
  • Part 245: An advertising line for Gibson guitars.
  • Part 258: “Nobody Knows,” by Kevin Sharp.
  • Part 262: “Dust in the Wind,” by Kansas.

DeMorgan’s Laws:

  • Part 5: “Never Gonna Give You Up,” by Rick Astley
  • Part 28: “We’re Breaking Free,” from High School Musical (2006)
  • Part 255: A line from “The Nightmare Before Christmas.”
  • Part 257: A line from “The Wizard of Oz.”

Simple nested predicates:

  • Part 6: “Everybody Loves Somebody Sometime,” by Dean Martin
  • Part 25: “Every Valley Shall Be Exalted,” from Handel’s Messiah
  • Part 33: “Heartache Tonight,” by The Eagles
  • Part 38: “Everybody Needs Somebody To Love,” by Wilson Pickett and covered in The Blues Brothers (1980)
  • Part 46: “Mean,” by Taylor Swift
  • Part 56: “Turn! Turn! Turn!” by The Byrds
  • Part 63: P. T. Barnum.
  • Part 64: Abraham Lincoln.
  • Part 66: “Somewhere,” from West Side Story.
  • Part 71: “Hold On,” by Wilson Philips.
  • Part 80: Liverpool FC.
  • Part 84: “If You Leave,” by OMD.
  • Part 103: “The Caisson Song” (US Army).
  • Part 111: “Always Something There To Remind Me,” by Naked Eyes.
  • Part 121: “All the Right Moves,” by OneRepublic.
  • Part 126: Motif from Hamilton.
  • Part 157: “Whenever, Wherever,” by Shakira.
  • Part 158: “Church Bells,” by Carrie Underwood.
  • Part 163: A famous line from The Princess Bride.
  • Part 170: “Everywhere,” by Tim McGraw.
  • Part 173: “If I Ain’t Got You,” by Alicia Keys.
  • Part 187: “Always Something There To Remind Me,” by Naked Eyes.
  • Part 198: “All Star,” by Smash Mouth.
  • Part 203: “Lean On Me,” by Bill Withers.
  • Part 217: A line in the video game Valorant.
  • Part 219: “Señorita,” by Shawn Mendes and Camila Cabello.
  • Part 220: “How to Love,” by Cash Cash.
  • Part 221: A line from Monk.
  • Part 237: A line from Psycho.
  • Part 254: “You Can’t Always Get What You Want,” by the Rolling Stones.
  • Part 256: “Irgendwie, Irgendwo, Irgendwann” by Nena.
  • Part 266: “Kokomo,” by the Beach Boys.

Maximum or minimum of a function:

  • Part 12: “For the First Time in Forever,” by Kristen Bell and Idina Menzel and from Frozen (2013)
  • Part 19: “Tennessee Christmas,” by Amy Grant
  • Part 22: “The Most Wonderful Time of the Year,” by Andy Williams
  • Part 48: “I Got The Boy,” by Jana Kramer
  • Part 60: “I Loved Her First,” by Heartland
  • Part 92: “Anything You Can Do,” from Annie Get Your Gun.
  • Part 119: “Uptown Girl,” by Billy Joel.
  • Part 124: “All I Want To Do Is Be With You,” from High School Musical 3.
  • Part 160: “God, Your Mama, and Me,” by Florida Georgia Line and the Backstreet Boys.
  • Part 178: “Ex Factor,” by Lauryn Hill.

Somewhat complicated examples:

  • Part 11 : “Friends in Low Places,” by Garth Brooks
  • Part 27 : “There is a Castle on a Cloud,” from Les Miserables
  • Part 41: Winston Churchill
  • Part 44: Casablanca (1942)
  • Part 51: “Everybody Wants to Rule the World,” by Tears For Fears
  • Part 58: “Fifteen,” by Taylor Swift
  • Part 59: “We Are Never Ever Getting Back Together,” by Taylor Swift
  • Part 61: “Style,” by Taylor Swift
  • Part 67: “When I Think Of You,” by Janet Jackson.
  • Part 78: “Nothing’s Gonna Stop Us Now,” by Starship.
  • Part 89: “No One Is Alone,” from Into The Woods.
  • Part 110: “Everybody Loves My Baby,” by Louis Armstrong.
  • Part 134: A famous line from Braveheart.
  • Part 141: “How Far I’ll Go,” from Moana.
  • Part 148: “The Climb,” by Miley Cyrus.
  • Part 153: “I Can’t Tell You Why,” by The Eagles.
  • Part 161: “For What It’s Worth,” by Buffalo Springfield.
  • Part 164: “When The Sun Goes Down,” by Kenny Chesney.
  • Part 199: “Never Say Never,” by Justin Bieber.
  • Part 213: “Sign of the Times,” by Harry Styles.
  • Part 241: “Dreams,” by Fleetwood Mac.
  • Part 267: A line from The Hound of the Baskervilles.

Fairly complicated examples:

  • Part 17 : Richard Nixon
  • Part 47: “Homegrown,” by Zac Brown Band
  • Part 52: “If Ever You’re In My Arms Again,” by Peabo Bryson
  • Part 83: “Something Good,” from The Sound of Music.
  • Part 85: “Joy To The World,” by Three Dog Night.
  • Part 88: “Like A Rolling Stone,” by Bob Dylan.
  • Part 91: “Into the Fire,” from The Scarlet Pimpernel.
  • Part 128: “A Puzzlement,” from The King and I.
  • Part 156: “Everybody Loves a Lover,” by Doris Day.
  • Part 159: “Fastest Girl in Town,” by Miranda Lambert.
  • Part 171: “Everybody’s Got Somebody But Me,” by Hunter Hayes.

Really complicated examples:

  • Part 18: “Sleigh Ride,” covered by Pentatonix
  • Part 26: “All the Gold in California,” by the Gatlin Brothers
  • Part 40: “One of These Things Is Not Like the Others,” from Sesame Street
  • Part 42: “Take It Easy,” by The Eagles

Parabolas from String Art: Index

I’m doing something that I should have done a long time ago: collecting a series of posts into one single post. The links below show my series on numerical integration.

Part 1: Introduction

Part 2: Identifying the highest points of the strings

Part 3: These nine points lie on a parabola: Method #1

Part 4: These nine points lie on a parabola: Method #2

Part 5: These nine points lie on a parabola: Method #3

Part 6: Proof that all of the highest points lie on a parabola without calculus, Part 1

Part 7: Proof that all of the highest points lie on a parabola without calculus, Part 2

Part 8: Proof that all of the highest points lie on a parabola with calculus

Part 9: Proof that the strings are indeed tangent to the parabola, with calculus

Part 10: Conclusion

Square roots and Logarithms Without a Calculator: Index

I’m doing something that I should have done a long time ago: collect past series of posts into a single, easy-to-reference post. The following posts formed my series on computing square roots and logarithms without a calculator (with the latest post added).

Part 1: Method #1: Trial and error.

Part 2: Method #2: An algorithm comparable to long division.

Part 3: Method #3: Introduction to logarithmic tables.

Part 4: Finding antilogarithms with a table.

Part 5: Pedagogical and historical thoughts on log tables.

Part 6: Computation of square roots using a log table.

Part 7: Method #4: Slide rules

Part 8: Method #5: By hand, using a couple of known logarithms base 10, the change of base formula, and the Taylor approximation \ln(1+x) \approx x.

Part 9: An in-class activity for getting students comfortable with logarithms when seen for the first time.

Part 10: Method #6: Mentally… anecdotes from Nobel Prize-winning physicist Richard P. Feynman and me.

Part 11: Method #7: Newton’s Method.

Part 12: Method #8: The formula \sqrt{b} \approx \displaystyle \frac{a+b}{2\sqrt{a}}

Thoughts on Numerical Integration: Index

I’m doing something that I should have done a long time ago: collecting a series of posts into one single post. The links below show my series on numerical integration.

Part 1 and Part 2: Introduction

Part 3: Derivation of left, right, and midpoint rules

Part 4: Derivation of Trapezoid Rule

Part 5: Derivation of Simpson’s Rule

Part 6: Connection between the Midpoint Rule, the Trapezoid Rule, and Simpson’s Rule

Part 7: Implementation of numerical integration using Microsoft Excel

Part 8, Part 9, Part 10, Part 11: Numerical exploration of error analysis

Part 12 and Part 13: Left endpoint rule and rate of convergence

Part 14 and Part 15: Right endpoint rule and rate of convergence

Part 16 and Part 17: Midpoint Rule and rate of convergence

Part 18 and Part 19: Trapezoid Rule and rate of convergence

Part 20 and Part 21: Simpson’s Rule and rate of convergence

Part 22: Comparison of these results to theorems found in textbooks

Part 23: Return to Part 2 and accuracy of normalcdf function on TI calculators

Adding by a Form of 0: Index

I’m doing something that I should have done a long time ago: collecting a series of posts into one single post. The following links comprised my series on adding by a form of 0 (analogous to multiplying by a form of 1).

Part 1: Introduction.

Part 2: The Product and Quotient Rules from calculus.

Part 3: A formal mathematical proof from discrete mathematics regarding equality of sets.

Part 4: Further thoughts on adding by a form of 0 in the above proof.