Mathematics scientific algebra

This chapter will review the fundamental mathematical concepts (algebra and trigonometry) needed for a quantitative understanding of college-level chemistry and physics. Virtually all of this material is covered in high-school mathematics classes, but often the connection to real scientific applications is not obvious in those classes. In contrast, the examples used here will frequently involve chemical and physical concepts that will be covered in detail in later chapters or in the later parts of a standard freshman chemistry book. Here they will be treated as math problems later you will see the underlying chemistry. 

This appendix introduces two mathematics topics important for chemistry stndents (1) scientific algebra and (2) electronic calculator mathematics. The scientific algebra section (Section A.l) presents the relationships between scientific algebra and ordinary algebra. The two topics are much more similar than different however, because everyone already knows ordinary algebra, the differences are emphasized here. The scientific calculator section (Section A.2) discusses points with which students most often have trouble. This section is not intended to replace the instruction booklet that comes with the calculator, but to emphasize the points in that booklet that are most important to science students. 

Chemistry and physics are both very logical sciences, but both depend on math to translate concepts into application. Unfortunately, many students who struggle in these disciplines have more trouble with the mathematics than with the scientific concepts. Therefore, let us begin our exploration of chemistry and physics with a review of some basic math skills and concepts that you will use throughout this course. While this chapter reviews basic math skills, it cannot replace a basic understanding of college-level algebra. 

This book is designed to help you leam the fundamentals of chemistry. To be successful, you must master the concepts of chemistry and acquire the mathematical skills necessary to solve problems in this quantitative science. If your algebra is rusty, you should polish it up. Appendix 1 reviews the algebra used in basic chemistry and also shows how to avoid mistakes while solving chemistry problems with your scientific calculator. The factor label method is introduced in Chapter 2 to show you how to use units to help with problem solutions. You can help yourself by using the standard symbols and abbreviations for various quantities (such as m for mass, m for meter, mol for moles, and M for molarity). Always use the proper units with your numerical answers it makes a big difference whether your roommate s pet is 6 inches long or 6 feet long ... 

The knowledge and use of basic mathematical concepts and skills is a necessary aspect of scientific study. Science depends on data and the manipulation of data requires knowledge of mathematics. Scientists often use basic algebra to solve scientific problems and design experiments. For example, the substitution of variables is a common strategy in experiment design. Also, the ability to determine the equation of a curve is valuable in data manipulation, experimentation, and prediction. 

Skill 5.3 Apply fundamental mathematical language, knowledge, and skills at the level of algebra and statistics in scientific contexts. 

Skill 18.1 Apply appropriate mathematical skills (e.g., algebraic operations, graphing, statistics, scientific notation) and technology to collect, analyze, and report data and to solve problems in chemistry. 

A compound statement such as The First International Conference on Numerical Algebra and Scientific Computing was held in 2006 and took place at the Institute of Computational Mathematics of the Chinese Academy of Sciences in New York can thus be easily analyzed, especially when written symbolically. The and connective indicates that the compound statement is a conjunction. Let/)be The First International Conference on Numerical Algebra and Scientific Computing was held in 2006, a true statement let q be (it) took place at the Institute of Computational Mathematics of the Chinese Academy of Sciences in New York, a false statement because the institute is in Beijing. The truth table for the conjunction indicates that the given compound statement is false T U F - F. 

Only a few basic mathematical skills are required for the study of general chemistry. But to concentrate your attention on the concepts of chemistry, you will find it necessary to have a firm grasp of these basic mathematical skills. In this appendix, we will review scientific (or exponential) notation, logarithms, simple algebraic operations, the solution of quadratic equations, and the plotting of straight-line graphs. 

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