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Course Criteria
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1.00 Credits
This course will examine mathematics as it appears in art and architecture. Topics will include geometric compass and straight-edge constructions, the use of special proportions in Renaissance buildings, the symmetries of architectural ornament, the Platonic solids, and the projective geometry behind perspective and its later conscious distortion in painting. 1.00 units, Lecture
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3.00 Credits
The sequence Mathematics 125-126 provides an opportunity to study differential calculus while simultaneously covering the needed skills from precalculus. Students who finish both Mathematics 125 and 126 will be prepared to take Mathematics 132, Calculus II. Topics in Mathematics 125 will include: the real number system; linear, quadratic, polynomial, rational, exponential, and trigonometric functions; equations and inequalities; limits and continuity; applications. Not open to students who have received credit for Mathematics 131. Ordinarily, this course, to be followed by Mathematics 126, is elected by students who need to take a course in calculus, but whose backgrounds in algebra and trigonometry need strengthening. 1.00 units, Lecture
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0.00 Credits
A continuation of Mathematics 125. Topics will include: the analytic geometry of lines, circles, and parabolas; functions and graphs; continuity; derivatives; and applications. Not open to students who have received credit for Mathematics 131. This course completes the sequence started in Mathematics 125. Together, Mathematics 125 and 126 combine a study of the differential calculus of functions of one variable with the necessary algebraic and trigonometric background. Prerequisite: Mathematics 125 with a grade of C- or better. 1.00 units, Lecture
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1.50 Credits
The real number system, functions and graphs, continuity, derivatives and their applications, antiderivatives, definite integrals, and the fundamental theorem of calculus. Mathematics, natural science, and computer science majors should begin the Mathematics 131, 132 sequence as soon as possible. Not open to students who have received credit for Mathematics 126 or who have received credit by successful performance on the Advanced Placement Examination of the CEEB (see Catalogue section "Advanced Placement for First-Year Students"). 1.50 units, Lecture
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50.00 Credits
Topics concerning the Riemann integral and its applications, techniques of integration, first-order ordinary differential equations, and sequences and series. Prerequisite: C- or better in Mathematics 126 or Mathematics 131, or an appropriate score on the AP Examination or Trinity's Mathematics Qualifying Examination. 1.50 units, Lecture
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3.00 Credits
This course is an accelerated version of Mathematics 132, which will cover in greater depth topics from that course, along with selected other topics from single-variable calculus. It is intended for those with strong Calculus I backgrounds; in particular, first-year students who have received credit via the Calculus AB Advanced Placement Examination should register for this course. Open to other students with permission of the instructor. See the description of Mathematics 132. Prerequisite: C- or better in Mathematics 126 or Mathematics 131, or an appropriate score on the AP Examination or Trinity's Mathematics Qualifying Examination. 1.50 units, Lecture
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50.00 Credits
Problems appear in every part of mathematics and often have an intrinsic beauty and appeal. Mathematical problem solving is not a distinct branch of mathematics, but rather is a "mindset" which combines results from all branches of mathematics with a collection of useful techniques and strategies. Attempts have been made to develop "systems" for problem solving, but for the most part facility is gained through experience. The purpose of this course is to develop skills in and foster an appreciation of mathematical problem solving. It will not be a "cookbook" course which teaches students to match stereotypical problems with canned solutions. Rather, the course will be a hands-on experience, and students will be expected to explore and present solutions to a wide variety of non-routine and challenging problems, both individually and in groups. Since the range of problems which a student can solve expands as a student masters more branches of mathematics, students can profitably repeat this course. This course may only be taken Pass/Fail and may be retaken for credit with permission of the departm Prerequisite: C- or better in Mathematics 126 or Mathematics 131, or an appropriate score on the AP Examination or Trinity's Mathematics Qualifying Examination. 0.50 units, Lecture
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1.00 Credits
This course deals with methods of proof and the nature of mathematical argument and abstraction. With a variety of results from modern and classical mathematics as a backdrop, we will study the roles of definition, example, and counterexample, as well as mathematical argument by induction, deduction, construction, and contradiction. 1.00 units, Lecture
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0.00 Credits
A proof-based course in linear algebra, covering systems of linear equations, matrices, determinants, finite dimensional vector spaces, linear transformations, eigenvalues, and eigenvectors. Prerequisite: C- or better in Mathematics 142 or a 200-level Mathematics course, or permission of the instructor. 1.00 units, Lecture
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50.00 Credits
Vector-valued functions, partial derivatives, multiple integrals, conic sections, polar coordinates, Green's Theorem, Stokes' Theorem, and Divergence Theorem. Prerequisite: C- or better in Mathematics 132 or 142. 1.50 units, Lecture
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