Life of Fred offers a Complete Math Education
from addition
through two years of calculus . . . and beyond.
---------more mathematics than any other curriculum we know of.
(It is recommended that the books be enjoyed in the order they are listed here.)
Go to the LOF Store to order our books. Visit the Where Should I Start page to choose a book.
High School MathematicsThis series cover the typical four years of high school with Beginning Algebra and Advanced Algebra, Trigonometry, and Geometry. Also listed here are the Calculus, Logic, and Statistic Texts. While written as college texts, they are all suitable for advanced upperclassman. Statistics (The first 5 chapters) and Logic (the first 6 chapters) in particular can be understood after completing algebra, while Calculus is best started after completing Geometry. (All the answers are given in each book. No need to buy answer keys, teachers' editions, or anything else.)
Life of Fred: Beginning Algebra Expanded Edition (Sample Pages)(This book replaces both Life of Fred: Beginning Algebra and Fred's Home Companion: Beginning Algebra. This book has all the Your Turn to Play problems completely worked out, which wasn't true in the old books. And it costs less.)
ISBN: 978-1-937032-11-1, hardback, 544 pages.
Zillions of Practice Problems for Beginning Algebra (Sample Pages)
Need a lot of practice or stuck on a particular kind of problem? This book has been requested by many readers. Keyed directly to the chapters and topics of the Beginning Algebra book. Each problem worked out in complete detail. Eleven mixture word problems are each worked out step by step, often using a whole page of explanation for each problem. Thirteen quadratic equations solved by completing the square. Thirteen examples of two equations with two unknowns solved by the elimination method. This book is mandatory for those who need it. The Zillions of Practice Problems Slogan: If your cat can work through all the problems in this book, your cat can teach Beginning Algebra at any school in the nation.
ISBN: 978-0-937032-04-3, hardback, 272 pages.
Life of Fred: Advanced Algebra Expanded Edition (Sample Pages)
All of second-year high school algebra: Ratios, Median averages, Proportions, Dividing by zero, Cross-multiplying, Constants of proportionality, Inverse variation, Direct variation, Joint variation, Weight varies directly as the cube of the height, Area varies directly as the square of the height, Volume varies directly as the cube of the height, Laws of exponents, Rationalizing the denominator, Pythagorean theorem, Solving radical equations, Surface area of a cone, A Brief History of mathematics, Natural numbers, Whole numbers, Integers, Irrational numbers, Real numbers, Imaginary numbers, Complex numbers, Velocity, Conversion factors, Unit analysis, Venn diagrams, Union of sets, Disjoint sets, Subsets, Intersection of sets, Significant digits in addition and multiplication, Scientific notation, Exponential equations, Logarithms, Product, quotient, birdie, and power rules for logarithms, Using a scientific calculator, Finding antilogs, Three definitions of logarithms, Change-of-base rule for logarithms, Graphing, Abscissa, Ordinate, Quadrants, Slope, Slope given two points, Slope-intercept and double-slope forms of the line, Slopes of perpendicular lines, Multiplying binomials, Factoring binomials, Factoring a difference of squares, Factoring trinomials, Adding, subtracting, multiplying and dividing polynomial fractions, Complex fractions, Linear equations, Quadratic equations, Radical equations, Systems of Equations, Inconsistent, dependent and independent equations, Graphing planes in three dimensions, Cramer’s rule, Determinants, Ellipses, Circles, Reflective property of ellipses, Parabolas, Hyperbolas, Graphing inequalities, Definition of a function, Domain, Codomain, Range, Functional notation, One-to-one, Onto, Inverse functions, Ordered pairs, Long division of polynomials, Partial fractions, Proofs by math induction, Linear Programming, Arithmetic progressions, and series, Adding and multiplying matrices, Geometric sequences and progressions, Sigma notation, Fundamental principle of counting, Factorial, Permutations, Combinations, Binomial formula, Pascal’s Triangle.
(This book replaces both Life of Fred: Advanced Algebra and Fred's Home Companion: Advanced Algebra. This book has all the Your Turn to Play problems completely worked out, which wasn't true in the old books. And it costs less.)
ISBN: 978-1-937032-13-5, hardback, 544 pages.
Zillions of Practice Problems Advanced Algebra (Sample Pages)
Need a lot of practice or stuck on a particular kind of problem? This book has been requested by many readers. Keyed directly to the chapters and topics of Life of Fred: Advanced Algebra. Each problem worked out in complete detail. Ten exponential equations worked out step by step. Over 40 problems dealing with functions. Sixteen imaginary number problems solved in detail. Eleven linear programming problems—each taking about a page to solve. A bonus six-page introduction to Turing Machines, starting on page 117.
ISBN: 978-0-937032-10-4, hardback, 240 pages.
Life of Fred: Geometry Expanded Edition (Sample Pages)
Thirteen regular chapters and six bonus honors chapters. Points and lines, Definition of when one point is between two other points, Definition of a triangle, Midpoint, Proof of a theorem in paragraph form, Tangent and secant lines, Area and volume formulas, Undefined terms, Hypothesis and conclusion, Contrapositives, Postulates, Euclid’s The Elements, Rays, Acute, obtuse, and right angles, Congruent angles, Linear pairs, Vertical angles, Supplementary angles, Perpendicular lines, SSS, SAS, ASA, Isosceles triangle theorem, Pons Asinorum, Parallel lines, Skew lines, Indirect proofs, Attempts to prove the parallel postulate, Exterior angles, Two proofs of the exterior angle theorem, Hypotenuse-leg theorem, Medians, Quadrilaterals: parallelogram, rhombus, trapezoid, kite, rectangle, square, Honor’s Problem of the century: If two angle bisectors are congruent when drawn to the opposite sides, then the triangle is isosceles, Definition of a polygon, Proofs of all the area formulas given only the area of a square (This is hard. Most books start with the area of a triangle as given.) Proofs of the Pythagorean theorem, Geometries with only three points, Similar triangles, Five manipulations of proportions, Angle bisector theorem, Symbolic logic, Truth tables, Circles, Inscribed angle theorem, Definition of a limit of a function, Inductive and deductive reasoning, Golden rectangles, 46 Ruler-and-compass constructions, Non-euclidean geometries, Solid geometry, Euler’s theorem, Geometry in high dimensions, Stereochemistry and homochirality, Complete chart up to the 14th dimension, Proofs using analytic geometry, Proof that a right angle is congruent to an obtuse angle using euclidean geometry, Flawless (modern) geometry which was invented about a hundred years ago.
ISBN: 978-1-937032-21-0, hardback, 560 pages.
Life of Fred: Trigonometry Expanded Edition (Sample Pages)
Additional notes from the author here
After Beginning Algebra, Advanced Algebra and Geometry, this book completes everything you need for calculus. Angles of elevation, Definition of the sine function, Angles of depression, Area of a triangle = ½ab sin θ, Heron’s formula, Review of graphing and significant digits, Discrete and continuous variables as illustrated in The Merchant of Venice, Tangent function, Why we create new mathematics, Limit of tan θ as θ approaches 90º, Ordinal and cardinal numbers, Cosine function, Graphing y = sin x, Identity function, Contrapositives, Domain and range of a function, Defining 6 to the pi power, Trig angles in standard position, Expanding the domain of a function, Periodic functions, Identities from algebra, Even and odd functions, Trig identities for sine and cosine, for tangent, for secant, Four suggestions for increasing success in solving trig identities, Trig identities for cotangent and cosecant, Nine tricks for solving trig identities, Shortcuts for graphing y = a sin (bx + c), Degrees, minutes, and seconds, Conversion factors, Radians, Videlicet, exempli. gratia, and id est, Area of a segment of a circle, Solving conditional trig equations, Related angles, Joseph Lister, Multiple angle formulas and their proofs, Symmetric law of equality, Probability of finding a right triangle, Law of Cosines, Florence Nightingale, Law of Sines, Inverse functions, One-to-one functions, Hyperbole, Principal values of the inverse trig functions, Ambiguous case for the law of sines, Why sin (2 Arctan 3) equals 3/5, Polar coordinates, Graphing a cardioid and a lemniscate, Codomain of a function, Official definition of the number one, Proof that the square root of 2 is irrational, Transcendental numbers, Complex numbers, Russell’s paradox, Malfatti’s problem and its solution in 1967, r cis θ, de Moivre’s theorem and its proof, The millionth roots of i, Review of the major parts of high school algebra and a preview of all of Calculus.
High School/University
Life of Fred: Logic (Sample Pages)
Suitable as a high school text (first six chapters) or as a college text (all 16 chapters)
Sentences in logic. Connectives. Inductive reasoning. Seventeen logic fallacies. Predicate logic. Syllogisms. Quantifiers. Proofs in predicate logic. Direct and indirect proofs. Set theory as a predicate logic structure. Axiom systems: consistent, complete, meaningful, independent, and recursive. Arithmetic model. Gödel numbering of symbols, sentences, and proofs. Proof of the Diagonal Lemma. Gödel’s Completeness theorem. Gödel’s two Incompleteness theorems and their proofs. Many puzzles (exercises) and their complete solutions.
Life of Fred: Statistics Expanded Edition (Sample Pages)
Suitable as a high school text (first 5 chapters) or a full year of college statistics.
Descriptive Statistics (averages, measures of dispersion, types of distributions), Probability, Bayes’ Theorem, From a Given Population Determine What Samples Will Look Like (7 tests), Techniques of Sampling, From a Given Sample Determine What the Population Was (14 tests), Determine Whether Two Given Samples Came From the Same Population (15 tests), Working With Three or More Samples (10 tests), Emergency Statistics Guide, Regression Equations, Field Guide, 16 Tables. (College level.)
Life of Fred: Calculus Expanded Edition (Sample Pages)
All of freshman and sophomore calculus.
Additional notes from the author here
Functions, Limits, Speed, Slope, Derivatives, Concavity, Trig, Related Rates, Curvature, Integrals, Area, Work, Centroids, Logs, Conics, Infinite Series, Solids of Revolution, Polar Coordinates, Hyperbolic Trig, Vectors, Partial Derivatives, Double Integrals, Vector Calculus, Differential Equations. (Sixteen units of college calculus.)