This is really a separate talk on what we can teach that adds value to students. My Academia. Mathematics Education and Philosophy of Mathematics Education. The Language of Mathematics more. Algebra is written in a symbolic language that is designed to express mathematical thoughts. This is a text for a course that emphasizes language skills.
Most math courses concentrate on computational skills; this one concentrates on how Most math courses concentrate on computational skills; this one concentrates on how mathematical methods and facts are expressed so you can understand what mathematical symbolism says. This course emphasizes all the ways that mathematics is used to express thoughts in algebra and higher-level classes. Mathematics Education. Instructor's Manual for "The Language of Mathematics" more. This file is a manual for instructors to teach them some of what they would know about the course if they had already taught it.
That is, it emphasizes how to read and write mathematics. Furthermore, it emphasizes how mathematical reasoning works. Proof: Introduction to Higher Mathematics more. This is a text for a course that introduces math majors and math-education majors to the basic concepts, reasoning patterns, and language skills that are fundamental to higher mathematics. The skills include the ability to read with The skills include the ability to read with comprehension, express mathematical thoughts clearly, reason logically, recognize and employ common patterns of mathematical thought, and read and write proofs.
To see another section, see Section 2. More Info: Co-authored with Norah C. Mathematics Education , Proof and Reasoning , and Mathematical reasoning and proof. Proof: Introduction to Higher Mathematics, Section 2. This is Section 2. Precalculus more. A text designed to produce a deep understanding of algebra and trigonometry so that students will be comfortable with their next math. Students will be well-prepared for calculus.
This text is designed to be appropriate for self-study, as This text is designed to be appropriate for self-study, as well as classroom use. Write me if you want to see some old exams or supplements.
Mathematics Education and Precalculus. How to Estimate the size of a coinage: Read these comments on the articles more. This is a page of notes on the differences between four articles on how to estimate the size of a coinage. The method in the article is preferred. This article gives a statistical method for estimating the number of dies used to strike issues of ancient coins and a demonstration that is it justified with real ancient-coin data.
Its mathematical justification is also noted. This method is shown to be better than previous methods, including my own methods published previously. The book is the proceedings of a conference of the same name held in Rome in Estimation of the size of a Coinage: A survey and comparison of methods more.
The discovery of the methods that does work well is in the paper. Use formula 4 in the article instead. Formula 4 is still the best way to give a confidence interval given the point estimate for the original number of dies. Formula 1 will give very similar results if the sample is random, but it never is.
For a confidence interval, use formula 4 in the article. Ancient Numismatics. The Theory of Linkage more. Linkage can help arrange dies in chronological order and help determine how the mint was organized. However, there are many caveats and typical deductions are often unwarranted unless the model of mint operation is remarkably simple. More Info: Published in the Numismatic Chronicle, , pages How to estimate the original number of dies and the coverage of a sample more.
Formulas for estimating the original number of dies from die-count data are given. The reasons they might not yield good estimates are discussed. Note: Although they were the best formulas known in , additional data suggests a Note: Although they were the best formulas known in , additional data suggests a method which is better. See my article, "The geometric model for estimating the number of dies.
Estimation of the number of dies used in a coinage when the sample has few duplicates more. Estimating the original number of dies from a sample with few or no duplicates is problematic. We cannot expect the "point estimate" to be at all precise If there are no duplicates it would be infinity! This paper discusses a formula for the confidence intervals. Statistics in Numismatics more.
Another Look at Daily Lotteries more. Publisher: eric. Algebra , Mathematics Education , and Cognitive Style. Votes or competitions which determine a winner by estimating expected plurality more. How can a "best" option be chosen by voting when not all voters have seen all options? For example, voters might vote for the "best film" from films they have seen, but not have seen all the films in contention. This article uses a This article uses a model of voting which is an extension to multiple options of the famous Bradley-Terry model.
Then the Maximum Likelihood Estimator is used. Page 1. Econometrics , Statistics , Degeneration , Odds ratio , Likelihood Function , and 2 more Matrix representation and maximum likelihood estimate Matrix representation and maximum likelihood estimate. Learning requires remembering. Calculators can help, if students have some way to summarize what they learn from many examples.
The symbolic language of algebra is a helpful tool. The Distribution of the numbers of coins struck by dies more. The number of coins struck before a die becomes unusable varies widely from die to die. Evidence from modern mint records and die-count data from ancient coins is used in an attempt to determine the distribution. Note: A great deal of Note: A great deal of additional data was considered in my article, "The geometric model for estimating the number of dies," which should be read after, or before, reading this article.
More Info: American Journal of Numismatics, second series , Pages Co-authored with Giles Carter. Weights of large numbers of coins can be difficult to summarize and interpret. Several ways to plot data are discussed and the Percentile Plot is recommended, especially for comparing weights of two or more issues. More Info: Published in the Numismatic Chronicle, The computer program in the Appendix is obsolete.
Statistical analysis of hoard data in ancient numismatics more. Discusses the difficulty of proving anything statistically from analysis of hoard data, especially about "loss" or "wastage" rates and the mobility of coins.
What can be done is discussed. Some novel methods of hoard analysis created by Some novel methods of hoard analysis created by Duncan-Jones are shown not to yield valid results. Low-silver Roman coins from the late third and early fourth centuries AD originally had a thin applied surface silvering.
The contribution of that silver to the total silver content is discussed. More Info: Published in the Numismatic Chronicle, , page Ancient Roman Numismatics. Co-authored with Nancy Equall and Richard J. The coverage of a random sample from a multinomial population is defined to be the sum of the probabilities of the observed classes. Five StarsBy T. PavacikJust as described4 of 4 people found the following review helpful. A "One of a Kind" TextbookBy Kindle CustomerThis is a brilliantly composed textbook the best I've seen on the market in the past 30 years ; it has gone through several editions over the years, primarily to fix typos.
The 6th edition should be free from all typos. This text is different from any other PreCalculus text on the market because its "take home" iPrecalculus book. Homepage Download PDF. Mobile pdf Precalculus 6th Edition. Copyright Disclaimer:This site does not store any files on its server.
We only index and link to content provided by other sites.
0コメント