Download Citation: Casella, G., & Berger, R. L. (2001). Statistical Inference. Duxbury Press. Chapter Summary: Chapter 1: Probability Theory Begins with the basics of probability theory, including definitions and properties of probability spaces, random variables, and common distribution functions. Chapter...
Download Citation: Mavrakakis, M. C., & Penzer, J. (2021). Probability and Statistical Inference: From Basic Principles to Advanced Models. Boca Raton, FL: Chapman and Hall/CRC. Chapter Summary: Chapter 1: Introduction Introduces the fundamental ideas of statistical inference, emphasizing the importance...
Download Citation: Rudin, W. (2024). Principles of Mathematical Analysis (3rd ed.). New York: McGraw-Hill, Inc. Chapter Summary: Chapter 1: The Real and Complex Number Systems Introduces real and complex numbers, focusing on their properties, operations, and the concept of ordered...
Download Citation: Wrede, R. (2010). Advanced Calculus (3rd ed.). Schaum’s Outline Series. McGraw-Hill. Chapter Summary: Chapter 1: Numbers Introduction to sets, real numbers, and the fundamental operations and properties within the real number system. It covers topics like decimal representation,...
Download Citation: Ostaszewski, A. (2009). Advanced Mathematical Methods (2nd ed.). Cambridge: Cambridge University Press. Chapter Summary: I. Linear Algebra: Chapters 1-9 delve into core concepts of vector spaces, including revisions of basic principles, matrices, spectral theory, and various forms of...
Download Citation: Anton, H. (2019). Elementary Linear Algebra (12th ed.). John Wiley & Sons. Chapter Summary: Chapter 1: Systems of Linear Equations and Matrices Introduces systems of linear equations and their representations using matrices. Key methods such as Gaussian elimination...
Download Citation: Bryant, V. (1990). Yet Another Introduction to Analysis. Cambridge University Press. Chapter Summary of "Yet Another Introduction to Analysis" by Victor Bryant: Chapter 1: Firm Foundations This chapter sets the stage by discussing the essential foundations of mathematical...
Download Citation: Liebeck, M. W. (2016). A Concise Introduction to Pure Mathematics (Fourth Edition). Boca Raton, FL: CRC Press. Chapter Summary: Chapter 1: Sets and Proofs Introduces basic set theory concepts, the language of sets, and fundamental proof techniques, establishing...
Download Citation: Allenby, R. B. J. T. (2003). Numbers and Proofs. Oxford: Butterworth-Heinemann. Chapter Summary: Chapter 1: The Need for Proof This chapter introduces the concept of proof, emphasizing its critical role in mathematics. It discusses the shift in teaching...
Download Citation Eccles, P. J. (2010). An Introduction to Mathematical Reasoning: Numbers, Sets, and Functions. Cambridge University Press. Chapter Summary Part I: Mathematical Statements and Proofs Chapter 1: The Language of Mathematics - Introduces the language and notation used in...