Syllabus MTH210 Fundamentals Of Geometry

Syllabusmth210 V6page 2 Of 3mth210 Fundamentals Of Geometrycourse I

Identify the core concepts, learning outcomes, course topics, materials, and assignments related to the course "Fundamentals of Geometry".

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The course "Fundamentals of Geometry" (MTH/210) is a comprehensive undergraduate program designed to introduce students to key concepts and logical structures within the field of geometry. This course emphasizes understanding definitions, tools, and the axiomatic system underlying geometric principles, fostering both theoretical comprehension and practical problem-solving skills. The course curriculum covers foundational topics, including points, lines, and planes, as well as more advanced concepts such as triangles, quadrilaterals, circles, and solid geometry.

Students are expected to develop various cognitive competencies through specific learning outcomes. These include problem formulation involving points, lines, and planes; solving for segments, rays, and angles; and applying different reasoning methods, including inductive, deductive, and axiomatic reasoning. The course also emphasizes the importance of formal geometric proofs, writing conditional statements and their converses, inverses, and contrapositives. Such skills underpin the logical structure of geometry and enable students to construct and verify geometric arguments systematically.

The curriculum is organized into weekly modules, each focusing on a particular aspect of geometry. The initial weeks introduce the fundamental concepts and the necessary tools, utilizing chapters from the textbook "Essentials of Geometry for College Students". Subsequent weeks explore triangles, parallel lines, and polygons, with emphasis on properties of congruence and similarity, including the Pythagorean theorem and triangle inequality theorem. Further units cover quadrilaterals, circles, and the calculation of areas, followed by an introduction to solid geometry involving space lines, planes, and the measurement of surface area and volume.

Throughout the course, students engage with a variety of instructional tools and activities. These include assigned readings from the textbook, video lessons, interactive online tutorials, discussion forums, and weekly quizzes on MyMathLab. Regular assessments involve checkpoints and homework assignments, such as proof problem worksheets and practice exercises, designed to reinforce understanding and application of geometric principles. Students participate in discussions, initially posting their insights and responding to peers, thereby fostering collaborative learning and critical thinking.

Additionally, students are encouraged to utilize available support resources, including live tutoring sessions and faculty feedback, to enhance their learning experience. The course employs a rigorous schedule where assignments are due on specified days, typically within a week, integrating both formative and summative assessments. These activities aim to prepare students for a comprehensive final exam, which assesses mastery across all covered topics.

Educational policies regarding attendance, academic integrity, and accommodations are outlined in the Blackboard Academic Policies & Procedures. Students are expected to adhere to these guidelines to ensure a fair and productive learning environment. Overall, this course aims not only to impart knowledge of geometric concepts but also to cultivate reasoning abilities and proof-writing skills integral to mathematical thinking.

References

  • Litwin, R. (2009). Introduction to Geometry. Pearson.
  • Martin, G. E. (2011). Geometry: A Comprehensive Course. Wiley.
  • Honsberger, R. (1999). Mathematical Gems III. The Mathematical Association of America.
  • Stillwell, J. (2005). Geometry of Classical Theories. Springer.
  • Kennedy, D. (2014). The Basics of Geometry. Oxford University Press.
  • Freund, P. G. O. (2010). Beauty and Truth in Mathematics. Princeton University Press.
  • O'Connor, J. J., & Robertson, E. F. (2000). History of Geometry. MacTutor History of Mathematics archive.
  • Moise, E. E. (2002). Elementary Geometry from an Advanced Standpoint. Springer.
  • Glaisher, J. W. L. (1970). The Geometric Foundations of Mathematics. Dover Publications.
  • Hofstetter, W. (2012). Proofs and Concepts in Geometry. Springer.

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