If you are a scientist, desiring to (re)build mathematical skills, a route:
1. George Simmons Precalculus in a Nutshell (~100 pages): can be read in an evening by the prepared, in a week by those who remember nothing. Gets the juices flowing, and there is zero fat in this very short text. This is all high school or middle school material, accessible to everyone. This book will show what you have forgotten.
2. Library of Mathematics. A series of short books (often ~80 pages) on particular topics, such as sequences and series, the complex numbers, the differential calculus, etc. They are concise, teach the essential instincts, but are generally not proof-based. Usually readable in a week.
3. Springers SUMS series (~200 pages). College mathematics, but typically gentle and written for self-study. Many titles are here, including calculus but much besides with nothing to do with calculus. In terms of a route, Introductory Mathematics: Algebra and Analysis and Introductory Mathematics: Applications and Methods serve as bridges from high school to college material.
Because linear algebra plays such a central role in applied mathematics, I'll mention
a) most algebra books have a chapter or two on linear algebra
b) SUMS Banchoff text is basic and anyone can start there
c) SUMS Blythe text is a good intro for the mathematically-minded
d) Strang's Linear Algebra is popular. My take: he's a gifted lecturer who recorded videos that went on YouTube and inspired millions, and I love the emphasis on factorization from the beginning, but the formatting can be off-putting; the lack of proofs is a boon for applied students and irritating for the mathematically-minded.
If you have not had calculus, Simmons has a good, interesting, but long text with answers for self-study; Spivak's and Apostol's texts are also excellent but for the more mathematically-minded.
To study the modeling and statistics used throughout applied science, you need linear algebra and calculus under your belt, there is no real alternative.
For the less hurried, you may enjoy the path I took: begin at Euclid's Elements (books I-VI, or more), proceed to Euler's Elements of Algebra, then as you like, for you are well-grounded historically at this point. Euclid is especially good if, for example, you map out the structure of dependence of proofs in a book. I spent time in the Anneli Lax series aiming at the high school/undergraduate transition with dives into interesting topics.
Titles pesonally recommended without hesitation:
Simmon's Precalculus in a Nutshell
Smith's Introductory Mathematics
Euclid's Elements
Euler's Elements of Algebra
Blythe's Linear Algebra
Niven's Counting without Counting
Old's Continued Fractions
Freedman's Statistics
Some lectures to jog memories about math fundamentals
001 Greatest common denominators (.pdf)
002 Numbers via infinity (.pdf)
003 Modulo (.pdf)
004 Permutation tests (.pdf)
005 Graphs (.pdf)
006 Ordering (.pdf)
007 Quadratics revisited (.pdf)
008 Quadratics, again (.pdf)
009 Geometry of i (.pdf)
010 Square roots, post-apocalypse (.pdf)
011 Null hypotheses (.pdf)
012 Euler number (.pdf)
1. George Simmons Precalculus in a Nutshell (~100 pages): can be read in an evening by the prepared, in a week by those who remember nothing. Gets the juices flowing, and there is zero fat in this very short text. This is all high school or middle school material, accessible to everyone. This book will show what you have forgotten.
2. Library of Mathematics. A series of short books (often ~80 pages) on particular topics, such as sequences and series, the complex numbers, the differential calculus, etc. They are concise, teach the essential instincts, but are generally not proof-based. Usually readable in a week.
3. Springers SUMS series (~200 pages). College mathematics, but typically gentle and written for self-study. Many titles are here, including calculus but much besides with nothing to do with calculus. In terms of a route, Introductory Mathematics: Algebra and Analysis and Introductory Mathematics: Applications and Methods serve as bridges from high school to college material.
Because linear algebra plays such a central role in applied mathematics, I'll mention
a) most algebra books have a chapter or two on linear algebra
b) SUMS Banchoff text is basic and anyone can start there
c) SUMS Blythe text is a good intro for the mathematically-minded
d) Strang's Linear Algebra is popular. My take: he's a gifted lecturer who recorded videos that went on YouTube and inspired millions, and I love the emphasis on factorization from the beginning, but the formatting can be off-putting; the lack of proofs is a boon for applied students and irritating for the mathematically-minded.
If you have not had calculus, Simmons has a good, interesting, but long text with answers for self-study; Spivak's and Apostol's texts are also excellent but for the more mathematically-minded.
To study the modeling and statistics used throughout applied science, you need linear algebra and calculus under your belt, there is no real alternative.
For the less hurried, you may enjoy the path I took: begin at Euclid's Elements (books I-VI, or more), proceed to Euler's Elements of Algebra, then as you like, for you are well-grounded historically at this point. Euclid is especially good if, for example, you map out the structure of dependence of proofs in a book. I spent time in the Anneli Lax series aiming at the high school/undergraduate transition with dives into interesting topics.
Titles pesonally recommended without hesitation:
Simmon's Precalculus in a Nutshell
Smith's Introductory Mathematics
Euclid's Elements
Euler's Elements of Algebra
Blythe's Linear Algebra
Niven's Counting without Counting
Old's Continued Fractions
Freedman's Statistics
Some lectures to jog memories about math fundamentals
001 Greatest common denominators (.pdf)
002 Numbers via infinity (.pdf)
003 Modulo (.pdf)
004 Permutation tests (.pdf)
005 Graphs (.pdf)
006 Ordering (.pdf)
007 Quadratics revisited (.pdf)
008 Quadratics, again (.pdf)
009 Geometry of i (.pdf)
010 Square roots, post-apocalypse (.pdf)
011 Null hypotheses (.pdf)
012 Euler number (.pdf)