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Life of Fred - Advanced Maths

Life of Fred - Advanced Maths is aimed at young people aged 17 and over and is roughly equivalent to "A" Level and higher college mathematics. Calculus (Expanded Edition)

by Stanley F. Schmidt Ph.D.

The Human Face of Calculus

All of Calculus! Sixteen college semester units including:

• Multi-variable Calculus
• Analytic Geometry
• Vector Calculus
• Differential Equations
• All fun! Just open & enjoy.

Topics covered:

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.

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This expanded edition includes all answers! Do not order the answer key with this book.

No. of pages: 592

Format: Hardback

Price: £39.00 Statistics (Expanded Edition)

by Stanley F. Schmidt Ph.D.

Lots of statistics and one morning in the life of six-year-old Fred.

• All the popular tests! Normal Distribution, Chi-Squared, etc.
• Regression equations!
• Emergency Statistics Guide!
• Field Guide!
• Topics covered:

Descriptive Statistics (averages, measures of dispersion, types of distributions), Probability, Bayes' Theorem, From a Given a 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.

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No. of pages: 576

Format: Hardback

Price: £39.00 Linear Algebra (Expanded Edition)

by Stanley F. Schmidt Ph.D.

The Human Face of Linear Algebra

Fred goes on a picnic with his two best friends. A college-level (post-calculus) course in Linear Algebra which includes all the standard topics . . .

• Systems of Equations with lots of ways to solve them
• All Kinds of SpacesVector, Inner Product, and Dual Spaces
• Linear Transformations including linear functionals
• All fun! Just open and enjoy.

Topics covered:

﻿Solving systems of equations with one, many, and no solutions. Gauss-Jordan elimination. Gaussian elimination. Matrices. LU-decomposition. Vector spaces. Inner product spaces. Gram-Schmidt orthogonalization process. Fourier series. Data fitting. Linear Transformations. Linear functionals. Dual spaces. Eigenvalues and eigenvectors. Markov chains.

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No. of pages: 368

Format: Hardback

Price: £42.00 Five Days of Upper Division Math

by Stanley F. Schmidt Ph.D.

Rather than a course of study, this book is a sampler of advanced math for students who love math and Fred and want to preview courses they may take later.

Upper division (college 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 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).

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No. of pages: 208

Format: Hardback

Price: £15.00 Real Analysis

by Stanley F. Schmidt Ph.D.

This book covers Real Analysis, a topic studied by math majors in college. This math is more advanced than what most non-majors ever see, but it still has Fred, and he has a very good time with his favorite topic. Real Analysis is the study of real numbers, functions using the real numbers, and the properties of the real numbers and their functions. It is heavy on theorems and proofs. Calculus is a requirement before studying this topic, and Life of Fred: Five Days is recommended.

Topics include:

• The Real Numbers
• Sequences
• Series
• Tests for Series Convergence
• Limits and Continuity
• Derivatives
• The Riemann Integral
• Sequences of Functions
• Series of Functions
• Two Cow-Moving Theorems
• Looking Ahead to Topics beyond a First Course in Real Analysis.
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