Solution Upper Intermediate Student 39;s Book Key

[Alayna Rother]

TheDepartment of Mathematics and Computer Science offers major programs leading to the bachelor of science in mathematics or the bachelor of science in computer science, as well as required and elective courses for students majoring in other fields. Either major may be pursued with any of three principal goals: preparation for graduate studies leading to advanced degrees in pure mathematics, applied mathematics, computer science, statistics, operations research, or other fields; preparation for secondary school teaching of mathematics or computer science; or preparation for a research career in business, industry, or government. The major in mathematics may be taken with an emphasis in applied mathematics, data science, financial mathematics, mathematical economics, or mathematics education. The emphasis in mathematics education is designed to prepare majors to take the California Subject Examination for Teachers (CSET). The major in computer science offers emphases specializing in algorithms and complexity, data science, security, software, or one of the student's choosing. Minors in mathematics or computer science are also available.

The Department of Mathematics and Computer Science maintains a program for the discovery, encouragement, and development of talent in mathematics or computer science among undergraduates. This program includes special sections, seminars, individual conferences, and directed study guided by selected faculty members. Students are also encouraged to participate actively in research projects directed by faculty.

In addition to fulfilling undergraduate Core Curriculum requirements for the bachelor of science degree, students majoring in mathematics or computer science must complete the following departmental requirements for the respective degree:

PHYS 31 and 32. Students with a special interest in the application of mathematics in the social sciences or economics may substitute ECON 170 or 173 for PHYS 32. Students planning to teach in secondary schools may substitute, with approval of the department chair, PHYS 11 and 12 for PHYS 31 and 32.

Individual emphasis of the student's choosing: In order to pursue this emphasis, a student must get their courses approved along with their advisor's signature at least three quarters before they graduate. Three of the five upper-division courses must be CSCI or MATH. The following are two examples:

For the major in either mathematics or computer science, at least four of the required upper-division courses in the major must be taken at Santa Clara. A single upper-division course in the Department of Mathematics and Computer Science may not be used to satisfy requirements for two majors or minors.

Three approved 5-unit upper-division mathematics courses with no more than one course selected from MATH 165 and 166. In place of MATH 165 or 166, a student may select an upper-division computer science course, but two of the three courses must be designated MATH. MATH 100, 192, 195, and CSCI 192 do not count toward the minor.

The State of California requires that students seeking a credential to teach mathematics or computer science in California secondary schools must pass the California Subject Examination for Teachers (CSET), a subject area competency examination. The secondary teaching credential additionally requires the completion of an approved credential program, which can be completed as a fifth year of study and student teaching, or through an undergraduate summer program internship. Students who are contemplating secondary school teaching in mathematics or computer science should consult with the coordinator in the Department of Mathematics and Computer Science as early as possible.

For students majoring in arts and humanities. Topics chosen from set theory, logic, counting techniques, number systems, graph theory, financial management, voting methods, and other suitable areas. Material will generally be presented in a setting that allows students to participate in the discovery and development of important mathematical ideas. Emphasis on problem solving and doing mathematics. (4 units)

Introduction to finite mathematics with applications to the social sciences. Sets and set operations, Venn diagrams, trees, permutations, combinations, probability (including conditional probability and Bernoulli processes), discrete random variables, probability distributions, and expected value. (4 units)

Elementary topics in statistics, including descriptive statistics, regression, probability, random variables and distributions, the central limit theorem, confidence intervals and hypothesis testing for one population and for two populations, goodness of fit, and contingency tables. (4 units)

College algebra and trigonometry for students intending to take calculus. Does not fulfill the undergraduate Core Curriculum requirement in mathematics. Requires enrollment in weekly lab session - MATH 9L. (4 units)

Focus on active learning to prepare students for calculus. Does not necessarily coordinate topics with Math 9 on a weekly basis. Instead, the lab sessions are designed to help students to build overall strength in non-routine problem solving. (1 unit)

Limits and differentiation. Methods and applications of differentiation. Ordinarily, only one of MATH 11, 30, or 35 may be taken for credit. Note: MATH 11 is not a suitable prerequisite for MATH 31 or 36 without additional preparation. Prerequisite: MATH 9 or a passing grade on the Calculus Readiness Exam. If MATH 9 is taken, a grade of C- or higher is strongly recommended before taking MATH 11. (4 units)

Further applications of differentiation. Integration and the fundamental theorem of calculus. Methods and applications of integration. Only one of MATH 12, 31, or 36 may be taken for credit. Note: MATH 30 and 35 are not suitable prerequisites for MATH 12 without additional preparation. Prerequisite: MATH 11 or equivalent. A grade of C- or higher in MATH 11 is strongly recommended before taking MATH 12. (4 units)

Taylor series, vectors, quadric surfaces, and partial derivatives, including optimization of functions with multiple variables. Prerequisite: MATH 12 or equivalent. Students who have taken Math 31, Math 36, or an equivalent course may take Math 13 after consultation with an instructor. A grade of C- or higher in MATH 12 is strongly recommended before taking MATH 13. (4 units)

Explicit solution techniques for first order differential equations and higher order linear differential equations. Use of numerical and Laplace transform methods. Only one of MATH 22, 23, or AMTH 106 may be taken for credit. Prerequisite: MATH 13. (4 units)

Sequences, series, and analytic functions. Use of explicit, numerical, and series methods to solve ordinary differential equations. Complex numbers. Only one of MATH 22, 23, or AMTH 106 may be taken for credit. Prerequisite: MATH 13. (4 units)

Differentiation and its applications to business, including marginal cost and profit, maximization of revenue, profit, utility, and cost minimization. Natural logarithms and exponential functions and their applications, including compound interest and elasticity of demand. Study of the theory of the derivative normally included in MATH 11, except trigonometric functions not included here. Ordinarily, only one of MATH 11, 30, or 35 may be taken for credit. Note: MATH 30 is not a suitable prerequisite for MATH 12 or 36 without additional preparation. Prerequisite: MATH 9 or a passing grade on the Calculus Readiness Exam. If MATH 9 is taken, a grade of C- or higher is strongly recommended before taking MATH 30. (4 units)

Modeling with functions, limits, and derivatives. Derivative rules and tools. Applications to the life sciences. Ordinarily, only one of MATH 11, 30, or 35 may be taken for credit. Note: MATH 35 is not a suitable prerequisite for MATH 12 or 31 without additional preparation. Prerequisite: MATH 9 or a passing grade on the Calculus Readiness Exam. If MATH 9 is taken, a grade of C- or higher is strongly recommended before taking MATH 35. (4 units)

Integration, differential equations, and probability. Applications to the life sciences. Only one of MATH 12, 31, or 36 may be taken for credit. Note: MATH 11 and 31 are not suitable prerequisites for MATH 36 without additional preparation. Prerequisite: MATH 35 or equivalent. A grade of C- or higher in MATH 35 is strongly recommended before taking MATH 36. (4 units)

Predicate logic, methods of proof, sets, functions, sequences, modular arithmetic, cardinality, induction, elementary combinatorial analysis, recursion, and relations. Also listed as COEN 19. (4 units)

Note: Although CSCI 10 is not explicitly listed as a formal prerequisite, some upper-division courses suggested for computer science majors may presuppose the ability to write computer programs in some language. A number of upper-division courses do not have specific prerequisites. Students planning to enroll should be aware, however, that all upper-division courses in mathematics require some level of maturity in mathematics. Those without a reasonable background in lower-division courses are advised to check with instructors before enrolling.

An introduction to writing and research in mathematics. Techniques in formulating research problems, standard proof methods, and proof writing. Practice in mathematical exposition for a variety of audiences. Strongly recommended for mathematics and computer science majors beginning their upper-division coursework. MATH 100 may not be taken to fulfill any mathematics or computer science upper-division requirements for students majoring or minoring in mathematics or computer science. Offered on demand. Prerequisites: CTW 1, CTW 2. (5 units)

Topics to be chosen from the following: Open and closed subsets of $R^n$, the definition of limits and continuity for functions on $R^n$, the least upper bound property on R, the intermediate and extreme value theorems for functions on $R^n\ $, the derivative of a function on $R^n$ in terms of a matrix, the matrix interpretation of the chain rule, Taylor\'s theorem in multiple variables with applications to critical points, the inverse and implicit function theorems, multiple integrals, line and surface integrals, Green\'s theorem, Stokes\' theorem, the divergence theorem, and differential forms. Prerequisites: MATH 14, 51, and 53. (5 units)

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