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.

Life of Fred: Logic (Sample Pages)

Suitable as a high school text (first six chapters) or as a college text (all 16 chapters)

Life of Fred: Statistics Expanded Edition (Sample Pages)

Suitable as a high school text (first 5 chapters) or a full year of college statistics.

Life of Fred: Calculus Expanded Edition (Sample Pages)

All of freshman and sophomore calculus.

Life of Fred: Five Days of Upper Division Math: Set Theory, Modern Algebra, Abstract Arithmetic, Topology (Sample Pages)
Upper division (junior/senior) pure math is much different than calculus. No “word problems,” no formulas to memorize, no concrete applications—just puzzles to solve. Instead of learning procedures, students create definitions, theorems, and proofs.
These are the first five days of Fred’s teaching set theory, modern algebra, abstract arithmetic, and topology. Each of the 139 assignments/puzzles/questions that he gives his students calls for creativity rather than doing drill work. Some of these can be done in a minute. Some will take several hours to complete. They are all meant to be enjoyed. The goal is not to finish the book. It’s just like life.
      The first day of set theory: cardinality of a set, set builder notation, naive set theory, modus ponens, seven possible reasons to give in a math proof, the high school geometry postulates are inconsistent, the proof that every triangle is isosceles, normal sets.
      The first day of modern algebra: definition of a math theory, six properties of equality, formal definition of a binary operation, formal definition of a function, definition of a group, right cancellation law, left inverses, commutative law.
      The first day of abstract arithmetic: circular definitions, unary operations, the successor function, natural numbers, the five Peano postulates, mathematical induction.
      The first day of topology: topology is all about friendship, listed and counting subsets, open sets, the discrete topology, the three axioms of a topology, models for a topology, open intervals.

      By the fifth day Fred will have covered the Schröder-Bernstein theorem (set theory), proved Lagrange’s theorem for subgroups of any group (modern algebra), defined the real numbers based only on the concept of “adding one” (abstract arithmetic), and explored continuous images of compact sets (topology).
ISBN: 978-1-937032-23-4, hardback, 208 pages.

Life of Fred: Abstract Algebra (Sample Pages)
Binary operations.  Groupoids.  Semigroups.  The Generalized Associative law.  Monoids.  Groups with left and right inverses, right cancelation, permutations.  Symmetric groups.  Cayley's theorem.  Subgroups and the Subgroup test.  Eleven facts about Cosets.  Partitions.  Lagrange's theorem and the order of a group.  Normal groups.  Factor groups.  Three super functions: isomorphisms, homomorphisms, and automorphisms.  Simple groups.  Hamiltonian groups.  Sporadic groups.  The Monster Group.  Inner automorphisms.  Kernels.  Fundamental Isomorphism Theorem of Group Homomorphisms. Center of group.  Centralizers.  Normalizers.  Direct product of groups.  Cyclic groups.  Fundamental Theorem of Finite Abelian Groups.  Sylow's three theorems.  Cauchy's theorem.  Rings.  Subrings.  Centers.  Direct sums.  Ideals.  Quotient rings.  Polynomial rings.  Integral domains.  Norm functions.  Euclidean domains.  Unique factorization domains.  Fields.  Field extentions.  Fundamental Theorem of Field Theory.  Algebraic and Transcendental extensions.  Vector spaces.
ISBN: 978-1-937032-64-7, hardback, 224 pages.

Life of Fred: Linear Algebra Expanded Edition (Sample Pages)

Usually taken in the junior (3rd) year    All the answers are given in the book.

Life of Fred: Real Analysis (Sample Pages)

      The Real Numbers, Sequences, Series, Tests for Series Convergence, Limits and Continuity, Derivatives, the Riemann Integral, Sequences of Functions, Series of Functions, and Looking Ahead to Topics beyond a First Course in Real Analysis.
      Subtopics include: The axiomatic approach to the real numbers, eleven properties of the real numbers, mathematics after calculus, definition of a function, if a and b are irrational, must ab also be irrational?, two definitions of dense subsets, the natural numbers are well-ordered, the positive real numbers are Archimedean—two definitions, math induction proofs, one-to-one (injective) functions, cardinality of a set, four definitions of onto, finding a one-to-one onto function from (0, 1) to [0, 1], countable and uncountable sets, Root Test, Ratio Test, Integral Test, absolute and conditional convergence, weak and strong induction proofs, secant lines, limit proofs using ε and δ, eight theorems about limits and their proofs, lim g(f(x)) does not always equal g(lim f(x)), continuous functions, four theorems about pairs of continuous functions, the squeeze theorem, a very short proof that lim sin x = 0 as x approaches zero, two definitions of derivative, the delta process, the five standard derivative rules and their proofs, how much detail to put in a proof, Schwarzschild radii, converses, contrapositives, and inverses, Intermediate Value Theorem, Rolle’s theorem, Mean Value Theorem, L’Hospital’s rule, proving lim (sin θ)/θ = 1 in two steps, detailed definition of the Riemann integral, uniform continuity, Fundamental Theorem of Calculus, Cauchy sequence of functions, Cauchy series of functions, uniform convergence of a series of functions, Weierstrass M-test, power series, two formulas for the radius of convergence, taking derivatives and antiderivatives of a power series, Weierstrass Approximation theorem, finding an approximation for ln 5 on a desert island, and the Cantor set.
ISBN: 978-1-937032-52-4, hardback, 304 pages.

Life of Fred: Complex Analysis (Sample Pages)

Arithmetic in the complex plane. Conjugates and absolute value. Polar form. Complex functions. Graphing. Limits and derivatives. Cauchy-Riemann equations. Holomorphic functions. Regions, open sets, connected sets. Paths. Analytic functions. Integration along a path. Fundamental Theorem of Complex Integration. Piecewise smooth paths. Paths with corners or cusps. Cauchy’s theorem. Closed paths. Simple paths. Cauchy–Goursat theorem. Trig functions, exponents, and logs in the complex plane. Argument of a polar complex function. Morera’s theorem. Three kinds of isolated singular points. Order of a pole. Proving L’Hospital’s rule in the complex plane. Meromorphic functions. Casorati-Weierstrass theorem. Picard’s great theorem. Cauchy’s formula. Jordan curve theorem. Liouville theorem. Proof of the Fundamental Theorem of Algebra. Taylor series and Laurent series. Residue theorem. Analytic continuation. Riemann Zeta function. Conformal Mappings. Homotopic paths. Harmonic functions.
ISBN: 978-1-937032-61-6, hardback, 176 pages.

Life of Fred: Numerical Analysis (Sample Pages)

Solving every equation that is in the form f(x) = 0.  Bisection method.  Solving f(x) = 5.  Solve x to the x power equals 5. Solving f(x) = g(x).  Finding the value of cos(cos(cos(cos(cos(cos(cos(cos(cos(cos(cos(cos(x)))))))))))).  Secant method.  Newton method.  Finding the polynomial to interpolate five points.  The Lagrange polynomial.  Dealing with 900 points and no given f(x).  Splines.  Piecewise polynomial approximations.  Numerical integration.  Why Simpson's rule is true.  Numerical differentiation.  Monte Carlo methods.  First-order ordinary differential equations starting with y' = g(x).  Starting with y' = g(x, y).  Euler's method.  Runge-Kutta method.  Second-order differential equations.  Second-order boundary problems.  Second-order initial value problems.  Parabolic partial differential equations.  Elliptic partial differential equations.  Hyperbolic partial differential equations.
ISBN: 978-1-937032-62-3, hardback, 208 pages.

Life of Fred: Metamathematics (Sample Pages)

The subfields of math.  Turing machines definition.  Adding, subtracting, recognizing more than two symbols.  The impossibility of locating all the non-blank symbols on an input tape.  Turing machines with two tracks.  With two tapes.  Unary notation.  The universal computer.  Turing machines on an infinite checkerboard instead of a tape.  The halting problem.  Dealing with negative numbers, copying a number, multiplying, exponentiation, projection and constant functions, determining if x > y.  Doing logic computations.  Doing geometry.  True vs. provable.  Gödel's First and Second Incompleteness Theorems.  Computable functions defined.  The Church-Turing thesis.  Primitive recursive functions.  General recursive functions.  The Ackermann function.  Self-replicating machines.  P and NP functions.
ISB: 978-1-937032-63-0, hardback, 128 pages.