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...

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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...

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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...

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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,...

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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...

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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...

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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...

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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...

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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...

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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...

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