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E-raamat: Mathematics and Statistics for the Quantitative Sciences

  • Formaat: 472 pages
  • Ilmumisaeg: 12-Dec-2022
  • Kirjastus: Chapman & Hall/CRC
  • Keel: eng
  • ISBN-13: 9781000806014
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Mathematics and Statistics for the Quantitative SciencesSuurem pilt
  • Formaat: 472 pages
  • Ilmumisaeg: 12-Dec-2022
  • Kirjastus: Chapman & Hall/CRC
  • Keel: eng
  • ISBN-13: 9781000806014
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Mathematics and Statistics for the Quantitative Sciences was born from a radical reimagining of first-year mathematics. While calculus is often seen as the foundational mathematics required for any scientist, this often leads to mathematics being seen as some, ultimately useless, hoop that needs to be jumped through in order to do what someone really wants to do. This sentiment is everywhere at every level of education. It even shows up in how people stereotype mathematics courses.

What this book aims to do, therefore, is serve as a foundational text in everyday mathematics in a way that is both engaging and practically useful. The book seeks to teach the mathematics needed to start to answer fundamental questions like why or how. Why do we only need to take census data once every few years? How do we determine the optimal dosing of a new pharmaceutical without killing people in the process? Or, more generally, what does it even mean to be average? Or what does it mean for two things to actually be different? These questions require a different way of thinking a quantitative intuition that goes beyond rote memorization and equips readers to meet the quantitative challenges inherent in any applied discipline.

Features





Draws from a diverse range of fields to make the applications as inclusive as possible Would be ideal as a foundational mathematical and statistical textbook for any applied quantitative science course
Preface xiii
Author Bio xvii
Section I Applied Mathematics
The Plot (so you don't lose it)
3(2)
Chapter 1 Functions
5(62)
1.1 Anatomy Of A Function
5(7)
1.2 Modelling With Mathematics
12(5)
1.3 Constants And Linear Functions
17(2)
1.4 Polynomials
19(7)
1.5 Exponentials And Logarithms
26(10)
1.6 Functions In Higher Dimensions
36(8)
1.7 Contour Diagrams
44(4)
1.8 Models In Two Dimensions
48(2)
1.9 Variables Vs. Parameters
50(17)
Chapter 2 Derivatives
67(52)
2.1 The Tangent Line
68(5)
2.2 Approximating Derivatives Of Functions
73(1)
2.3 Limits
73(6)
2.4 Limits And Derivates
79(1)
2.5 Derivative Formulas
80(4)
2.6 The Product Rule
84(3)
2.7 The Chain Rule
87(6)
2.8 Mixing Rules
93(4)
2.9 Critical Values
97(5)
2.10 Constrained Optimization
102(6)
2.11 Elasticity
108(3)
2.12 Partial Derivatives
111(8)
Chapter 3 Linear Algebra
119(42)
3.1 Vectors
119(16)
3.2 Matrices
135(3)
3.3 Multiplication: Numbers And Matrices
138(1)
3.4 Multiplication: Matrix And Vectors
138(4)
3.5 Multiplication: Matrix And Matrix
142(1)
3.6 Leslie Matrices
142(3)
3.7 The Determinant
145(5)
3.8 Eigenvalues & Eigenvectors
150(11)
Chapter 4 Derivatives in Multiple Dimensions
161(32)
4.1 Applications
176(7)
4.2 Distribution Fitting, Probability, And Likelihood
183(10)
Chapter 5 Differential Equations
193(20)
5.1 Solving Basic Differential Equations: With An Example
196(2)
5.2 Equilibria And Stability
198(6)
5.3 Equilibria And Linear Stability In Higher Dimensions
204(2)
5.4 The Jacobian
206(7)
Chapter 6 Integration
213(24)
6.1 Accumulated Change
213(5)
6.2 The Fundamental Theorem Of Calculus
218(1)
6.3 The Anti-Derivative
219(3)
6.4 Fundamental Theorem Of Calculus Revisited
222(2)
6.5 Properties Of Integrals
224(2)
6.6 Integration By Parts
226(3)
6.7 Substitution
229(8)
Section II Applied Stats & Data
Science Some Context to Anchor Us
237(2)
Math Versus The World
239(4)
Chapter 7 Data and Summary Statistics
243(32)
7.1 What Is Data?
243(7)
7.2 Data In Python
250(4)
7.3 Summary Statistics
254(6)
7.4 Ethical And Moral Considerations: Part 1
260(1)
7.5 Mean Vs. Median Vs. Mode
261(1)
7.6 Variance And Standard Deviation
261(4)
7.7 Ethical And Moral Considerations: Episode 2
265(1)
7.8 An Example
266(4)
7.9 The Empirical Rule
270(5)
Chapter 8 Visualizing Data
275(20)
8.1 Plotting In Python
277(1)
8.2 Scatter Plots
277(2)
8.3 Outliers
279(3)
8.4 Histograms
282(5)
8.5 The Anatomy Of A Technical Document
287(4)
8.6 Bad Plots And Why They're Bad
291(4)
Chapter 9 Probability
295(36)
9.1 Ethical And Moral Considerations: A Very Special Episode
295(1)
9.2 Counting
296(2)
9.3 Permutations
298(1)
9.4 Combinations
299(3)
9.5 Combinations With Replacement
302(3)
9.6 Probability
305(7)
9.7 Properties Of Probabilities
312(2)
9.8 More Notation
314(5)
9.9 Conditional Probability
319(2)
9.10 Bayes' Theorem
321(1)
9.11 The Prosecutor's Fallacy
322(5)
9.12 The Law Of Total Probability
327(4)
Chapter 10 Probability Distributions
331(56)
10.1 Discrete Probability Distributions
332(2)
10.2 The Binomial Distribution
334(4)
10.3 Trinomial Distribution
338(2)
10.4 Cumulative Probability Distributions
340(4)
10.5 Continuous Probability
344(2)
10.6 Continuous Vs. Discrete Probability Distributions
346(1)
10.7 Probability Density Functions
347(4)
10.8 The Normal Distribution
351(5)
10.9 Other Useful Distributions
356(6)
10.10 Mean, Median, Mode, And Variance
362(3)
10.11 Summing To Infinity
365(3)
10.12 Probability And Python
368(10)
10.13 Practice Problems
378(9)
Chapter 11 Fitting Data
387(50)
11.1 Defining Relationships
387(1)
11.2 Data And Lines
388(14)
11.3 Distribution Fitting And Likelihood
402(4)
11.4 Dummy Variables
406(6)
11.5 Logistic Regression
412(2)
11.6 Logistic Regression In Python
414(2)
11.7 Iterated Logistic Regression
416(2)
11.8 Random Forest Classification
418(2)
11.9 Bootstrapping And Confidence Intervals
420(11)
11.10 T-Statistics
431(3)
11.11 The Dichotomous Nature Of P-Values
434(3)
Appendix A A Crash Course in Python
437(10)
A.I Variables
438(1)
A.II Keywords
439(1)
A.III Conditionals
439(1)
A.V Loops
440(1)
A.V Import
441(2)
A.VI Functions
443(2)
A.VII A Simple Python Program
445(2)
Bibliography 447(4)
Index 451
Matthew Betti is an applied mathematician focusing on mathematical modeling of ecological and evolutionary problems, and disease spread. He is currently situated in Sackville, NB at Mount Allison University where he has developed and taught most first year courses in mathematics and computer science. Betti focuses on blending the rigourous with the intuitive to renew interesting in mathematics and statistics in students who see the subjects as a hurdle. Betti also incorporates discussions of ethics and social problems and the place of the mathematical sciences in this context.

Betti's research on disease spread and the ecology of honey bees has been published in numerous international journals. His approachable synthesis of complex material has been recognized by a number of presentation awards, and consultation work with governments at all levels.
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