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Fundamentals of Freshman Mathematics
Survey of mathematics designed to prepare the student for a course in analytic geometry and calculus
Hardcover
First published June 1, 1972
About the author
Carl B. Allendoerfer
10 booksCarl Barnett Allendoerfer (April 4, 1911 – September 29, 1974) was an American mathematician in the mid-twentieth century, known for his work in topology and mathematics education.
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Displaying 1 of 1 review
March 2, 2016
[Goodreads database is a later edition than I read]
Allendoerfer and Oakley, Fundamentals of Freshman Mathematics [second edition, 1965] 588 pages
Inspired by the Penrose book, I have begun a project of reviewing my high school and college mathematics, with the intention of going beyond them to the next steps. I decided to begin by re-reading my eleventh grade algebra book. The "freshman" in the title refers to college. There seem to be two meanings to the course name "College Algebra" depending on the college: it can mean high school algebra from a more rigorous standpoint, or what comes after high school algebra (i.e. abstract algebra). This is the first type; it would be a low level college text, sort of remedial for those whose high school math wasn't sufficient for calculus, but for high school it was fairly high level. It could probably best be considered as what used to be called "ATA" (Algebra-Trigonometry-Analysis); in present day terms, Precalculus plus a simplified version of the first month of calculus. The author's assumption is that the student will be going on to study science or engineering, rather than pure math, so it is written from that perspective.
Being written before the circa 1970 dumbing down of high school math, it begins with a brief introduction to logic and set theory, then gives a somewhat more advanced review of number systems and basic algebra (i.e. what today would be Pre-algebra, Algebra I and II), goes on to cover simultaneous equations and inequalities, vectors and matrices, exponential and logarithmic functions, and basic trigonometry, and ends with an intuitive introduction to limits, derivatives and integrals.
At some point, I acquired a second used copy of this, and used it for tutoring students who were returning to college after forgetting most of their high school math, or simply worried (rightly, usually) that their high school math courses were not an adequate preparation for college math.
The main "shortcoming" from a present day perspective is that there is nothing about how to do everything on a calculator (the introduction mentions that they are "far too expensive" for the average undergraduate!). There are also a few typos which affect the sense, especially in the equations.
Not the world's most interesting book, and somewhat less advanced than I remembered (some of what I thought I learned here I must have gotten later in my calculus courses), but a decent review of things I had partly forgotten (especially vectors and matrices.)
Allendoerfer and Oakley, Fundamentals of Freshman Mathematics [second edition, 1965] 588 pages
Inspired by the Penrose book, I have begun a project of reviewing my high school and college mathematics, with the intention of going beyond them to the next steps. I decided to begin by re-reading my eleventh grade algebra book. The "freshman" in the title refers to college. There seem to be two meanings to the course name "College Algebra" depending on the college: it can mean high school algebra from a more rigorous standpoint, or what comes after high school algebra (i.e. abstract algebra). This is the first type; it would be a low level college text, sort of remedial for those whose high school math wasn't sufficient for calculus, but for high school it was fairly high level. It could probably best be considered as what used to be called "ATA" (Algebra-Trigonometry-Analysis); in present day terms, Precalculus plus a simplified version of the first month of calculus. The author's assumption is that the student will be going on to study science or engineering, rather than pure math, so it is written from that perspective.
Being written before the circa 1970 dumbing down of high school math, it begins with a brief introduction to logic and set theory, then gives a somewhat more advanced review of number systems and basic algebra (i.e. what today would be Pre-algebra, Algebra I and II), goes on to cover simultaneous equations and inequalities, vectors and matrices, exponential and logarithmic functions, and basic trigonometry, and ends with an intuitive introduction to limits, derivatives and integrals.
At some point, I acquired a second used copy of this, and used it for tutoring students who were returning to college after forgetting most of their high school math, or simply worried (rightly, usually) that their high school math courses were not an adequate preparation for college math.
The main "shortcoming" from a present day perspective is that there is nothing about how to do everything on a calculator (the introduction mentions that they are "far too expensive" for the average undergraduate!). There are also a few typos which affect the sense, especially in the equations.
Not the world's most interesting book, and somewhat less advanced than I remembered (some of what I thought I learned here I must have gotten later in my calculus courses), but a decent review of things I had partly forgotten (especially vectors and matrices.)
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