Numbers and Operations (Annotated Bibliography Sample)

Running head: ANNOTATED BIBLIOGRAPY
Probability/Statistics and Algebra
Student’s name
Month date, YEAR
Institutional affiliation
DeGroot, M. H., & Schervish, M. J. (2012). Probability and statistics. Boston: Addison-Wesley.
The value of probability and statistics in manufacturing is fundamental. Mr. DeGroot was a renowned statistician from the 20th century. He founded the department of statistics in Carnegie Mellon University and also was the first editor of the statistical science. The book incorporates the Bayesian and classical methods of statistical analysis and data simulations. The book has bootstraps to help the readers’ gain better understanding of the topics. Some topics include linear models of residual data analysis with extensive examples with real data. The assumption made in the book is that the reader has an understanding of calculus and the concepts of matrices and vectors. The book also contains numerous graphical and real world examples. The book creates a steadfast foundation on the relevant topics practicality. The real world problems and solutions suggested in the book are useful to the teachers, students and researchers. Some of the topics are unique and rare in the introductory editions of probability and statistics. It includes sample survey analysis, quality statistical controls and experimental data analysis. This is the typical book that builds on the basics applying the advanced statistical methodologies in data analysis. The economic prospects of a nation can be assessed through graphical analysis of the stock market trends and classical data analysis initiatives. Experimental data analysis may involve a statistical survey of the future prospects among the youth and/or the life expectancy level of people from different nations.
Keele, L. (2015). The Statistics of Causal Inference: A View from Political Methodology. Political Analysis, 313-335. Retrieved from  HYPERLINK "http://pan.oxfordjournals.org/cgi/doi/10.1093/pan/mpv007" http://pan.oxfordjournals.org/cgi/doi/10.1093/pan/mpv007
Statistical analysis evidence is important in building a causal relationship case. On top of providing casual relationships statistical analysis can also be used as a source of casualty from the strong data indications even where casualty is inexistent. The writing by Keele provides statistics for the purpose of extrapolation of the casual information. Keele does not focus on any specific methods of statistical analysis but instead he focuses much of his time on the hypothesis that gives estimates from statistics casual interpretation. The assumptions made in interpreting statistical data in this text are known as identification assumption. The assumptions here in are fundamental in the analysis of statistical data on the casual effects. An extensive framework of the identification assumptions and the mention of an approach based on design for casual interpretation are applied in the text. An overview of the statistical techniques applied for casual interpretation of mathematical situations is included in the text. From the information derived from the text it is evident that statistical analysis could use some assumptions to better understand situations from different angles. The real world is faced by political and social situations that require the practical application of casual statistical analysis aimed at drawing an estimation of the prevailing situations. In America today there is a political atmosphere blooming and candidates are busy campaigning for the 2016 general elections. A casual statistical analysis based on sampling is applicable in estimating the performance of the candidates. Most often than not the analysis give a rough idea of the political prospects of the candidates.
Kinney, J. J. (2009). A probability and statistics companion. Hoboken, N.J: Wiley.
The author John J. Kinney is a professor at the Rose Hulman technological institute. He is an experienced mathematician having conducted extensive research in probability and statistics. He has written a number of journal articles and has also authored the book a probability: an introduction with statistical applications. The book a probability and statistics companion introduces the topic of statistics and probability in an exceptional fashion. The opening is interesting and captivating. The topics explored in the book include sample survey analysis and experiments. The major topics in probability and statistics are covered in the book. Some of the topics discussed include data analysis of sample surveys, experimental data analysis and control of statistical processes. The book introduces the reader to the contemporary design of scientific experiments and outlines the various sampling techniques in an understandable manner. The incorporation of the diverse topics in the book facilitates a deep understanding of the probability and statistics discipline. Each of the successive topics has an exercise for practice at the end. The exercises also serve as a guide to further reading and investigations. The book also contains graphs that are multidimensional to facilitate understanding of the examples.
Lee, L., & Freiman, V. (2006). Developing Algebraic Thinking through Pattern Exploration. Mathematics Teaching in the Middle School, 11, 428-433.
The journal article explores the working of patterns from the kindergarten level. The realization by teachers and researchers that students are enthusiastic about patterns is important. The flexibility of perception towards patterns requires comprehensive and intensive training. The selection of patterns that have mathematical relevance requires a good intuition. There may not be a direct relationship between the skills gained from patterns and algebra. The process of perceiving patterns and articulating the pattern and employing symbolism of algebra is what essentially comprises algebra. The rules of patterns involve use of quantity variables. Variables in learning patterns are mostly limited to numerals although students may familiarize themselves with the functions of variables in learning. The study of patterns according to Scaffolded can be a strong foundation for thinking in terms of algebra with relation to unknown variables, expressions, equivalence, manipulated symbols, range and domains of mathematical expressions and solving equations for unknown values. The article by Lee & Freiman (2006) employs the use of the T pattern on the how of formulating questions as a prerequisite of introducing the topic of algebra for the students in mid school.
The grip a learner has on mathematical expression and solutions to equations corresponds to the nature of the foundation given to the learner. A careful framing of young minds inclining them to persuasive and enthusiastic learning is important. The article by Lee & Freiman (2006) is a good basis upon which the national council of teachers of mathematics can build a strong foundation for the students. Algebra and algebraic equations can employ the background of patterns and bank on student’s enthusiasm towards patterns with the objective of increasing the level of understanding and speed up learning at the same time.
PEARL, J. (2000). Causality: models, reasoning, and inference. Cambridge, U.K., Cambridge University Press.
The book serves the purpose of advancing graphical tools in the assessment of casual analysis, development of algorithms applying the partial correlation method to explore casual structures under some presumptions, in depth discussion about casualty and development of parametric and nonlinear extension of semantics. The book is founded on the discipline of empirical research. The book is more useful for empirical research more than it is for statistics learning. Pearl endeavors to add on the value of statistics in research by going a notc...