Analytic Geometry(MAT116)
| Course Code | Course Name | Semester | Theory | Practice | Lab | Credit | ECTS |
|---|---|---|---|---|---|---|---|
| MAT116 | Analytic Geometry | 1 | 3 | 2 | 0 | 5 | 8 |
| Prerequisites | |
| Admission Requirements |
| Language of Instruction | |
| Course Type | Compulsory |
| Course Level | Bachelor Degree |
| Course Instructor(s) | Öznur TURHAN oturhan@gsu.edu.tr (Email) Can Ozan OĞUZ canozanoguz@gmail.com (Email) |
| Assistant | |
| Objective | Develop analytical tools to draw a connection between high school geometry, linear algebra and multivariable analysis |
| Content |
Plane Geometry -Coordinates in the plane (Cartesian and polar), -Vectors (arithmetic operations, dot product, determinant, orthogonality, linear dependence), -Complex numbers (arithmetic and geometry, polar representation), -Representations of lines in the plane (two points, one point and a direction vector, one point and a normal vector, Cartesian equation, parametric equation), -Analysis of the intersection of lines using systems of equations (Gaussian elimination, matrices, Cramer’s rule) Spatial Geometry (3D Geometry) -Coordinates in space (Cartesian, cylindrical, spherical), -Vectors (arithmetic operations, dot product, determinant, cross product, orthogonality, linear dependence), -Representations of lines and planes in space, -Methods for computing intersections, distances, and angles between lines and planes in space Conic Sections -Types of conics and their various representations (geometric, single-focus definition, double-focus definition, second-degree equations), -Classification of second-degree equations in two variables |
| Course Learning Outcomes |
1. Identify and define the various planar coordinate systems, apply them appropriately according to context, and perform transformations between these systems, 2. Master algebraic operations on vectors, including arithmetic operations, the dot product, the determinant, and the cross product, 3. Understand the geometric interpretations of vector operations and apply them effectively in relevant situations, 4. Represent lines and planes in multiple forms (vector, parametric, Cartesian, etc.) and convert between these representations, 5. Analyze the conditions of intersection between lines and planes using systems of linear equations, employing various solution methods (Gaussian elimination, matrix methods, Cramer’s rule), 6. Represent conic sections in different forms (geometric, algebraic, single-focus or double-focus definitions) and transition between these representations, 7. Classify second-degree equations in two variables based on their algebraic and geometric properties. |
| Teaching and Learning Methods | Theoric lectures, weekly practice sheets |
| References |
Shared lecture notes Géométrie, Cours et Exercices, A. Warusfel et al., Vuibert 2002 Géométrie élémentaire, André Gramain, Hermann, 1997. Précis de géométrie analytique, G.Papelier, Vuibert 1950. Exercises de géométrie analytique, P.Aubert, G.Papelier,Vuibert 1953. Cours de géométrie analytique, B. Niewenglowski, Gauthier-Villars, 1894. |
Theory Topics
| Week | Weekly Contents |
|---|---|
| 1 | Real line, Concept of a reference frame on a line and on a plane, Coordinate systems (Cartesian, polar) |
| 2 | Vectors (Concept of a vector in the plane, its formal definition, vector arithmetic, vector coordinates, linear (in)dependence) |
| 3 | The norm of a vector, dot product and determinant of two vectors, their geometric interpretations, Complex numbers |
| 4 | Arithmetic of complex numbers, Representation of lines in the plane |
| 5 | Intersection of lines, solving systems of linear equations, Introduction to matrices |
| 6 | Arithmetic of 2×2 matrices |
| 7 | Geometry of three-dimensional space (reference frames, coordinate systems, vectors, cross product, determinant) |
| 8 | Midtem |
| 9 | Representation of lines and planes, and their intersections |
| 10 | Intersections of lines and planes |
| 11 | Introduction to conic sections, study of types of conics |
| 12 | Study of conic sections |
| 13 | Classification of quadratic forms in two variables |
| 14 | Classification of quadratic forms in two variables |
Practice Topics
| Week | Weekly Contents |
|---|---|
| 1 | - |
| 2 | Real line, Concept of a reference frame on a line and on a plane, Coordinate systems (Cartesian, polar) |
| 3 | Vectors (Concept of a vector in the plane, its formal definition, vector arithmetic, vector coordinates, linear (in)dependence) |
| 4 | The norm of a vector, dot product and determinant of two vectors, their geometric interpretations, Complex numbers |
| 5 | Arithmetic of complex numbers, Representation of lines in the plane |
| 6 | Intersection of lines, solving systems of linear equations, Introduction to matrices |
| 7 | Arithmetic of 2×2 matrices |
| 8 | - |
| 9 | Geometry of three-dimensional space (reference frames, coordinate systems, vectors, cross product, determinant) |
| 10 | Representation of lines and planes, and their intersections |
| 11 | Intersections of lines and planes |
| 12 | Introduction to conic sections, study of types of conics |
| 13 | Study of conic sections |
| 14 | Classification of quadratic forms in two variables |
Contribution to Overall Grade
| Number | Contribution | |
|---|---|---|
| Contribution of in-term studies to overall grade | 11 | 60 |
| Contribution of final exam to overall grade | 1 | 40 |
| Toplam | 12 | 100 |
In-Term Studies
| Number | Contribution | |
|---|---|---|
| Assignments | 10 | 40 |
| Presentation | 0 | 0 |
| Midterm Examinations (including preparation) | 1 | 20 |
| Project | 0 | 0 |
| Laboratory | 0 | 0 |
| Other Applications | 0 | 0 |
| Quiz | 0 | 0 |
| Term Paper/ Project | 0 | 0 |
| Portfolio Study | 0 | 0 |
| Reports | 0 | 0 |
| Learning Diary | 0 | 0 |
| Thesis/ Project | 0 | 0 |
| Seminar | 0 | 0 |
| Other | 0 | 0 |
| Make-up | 0 | 0 |
| Toplam | 11 | 60 |
| No | Program Learning Outcomes | Contribution | ||||
|---|---|---|---|---|---|---|
| 1 | 2 | 3 | 4 | 5 | ||
| 1 | understands principles of deductive reasoning; has experience to verify well-foundedness and exactness of mathematical statements in systematic ways; | X | ||||
| 2 | can properly state and use concepts and results of major mathematical interest; | X | ||||
| 3 | masters current computational techniques and algorithms; has a good ability in their use; can identify relevant tools, among those one has learned, suitable to solve a problem and is able to judge whether or not one is in possession of these tools; | X | ||||
| 4 | is able to express one’s mathematical ideas in an organised way both in written and oral forms; | X | ||||
| 5 | understands relations connecting substantial concepts and results; can switch from one viewpoint to another on mathematical objects (pictures, formulae, precise statements, heuristic trials, list of examples,...); | X | ||||
| 6 | has followed individually a guided learning strategy; has pursued steps toward the resolution of unfamiliar problems; | X | ||||
| 7 | has a theoretical and practical knowledge in computer science well adapted for learning a programming language; | X | ||||
| 8 | has investigated the relevance of modeling and using mathematical tools in natural sciences and in the professional life; is conscious about historical development of mathematical notions; | X | ||||
| 9 | has followed introduction to some mathematical or non-mathematical disciplines after one’s proper choice; had experience to learn selected subjects according to one’s proper arrangement; | X | ||||
| 10 | masters French language as well as other foreign languages, to a level sufficient to study or work abroad. | X | ||||
| Activities | Number | Period | Total Workload |
|---|---|---|---|
| Class Hours | 14 | 5 | 70 |
| Working Hours out of Class | 14 | 4 | 56 |
| Assignments | 10 | 4 | 40 |
| Presentation | 0 | 0 | 0 |
| Midterm Examinations (including preparation) | 1 | 10 | 10 |
| Project | 0 | 0 | 0 |
| Laboratory | 0 | 0 | 0 |
| Other Applications | 0 | 0 | 0 |
| Final Examinations (including preparation) | 1 | 20 | 20 |
| Quiz | 0 | 0 | 0 |
| Term Paper/ Project | 0 | 0 | 0 |
| Portfolio Study | 0 | 0 | 0 |
| Reports | 0 | 0 | 0 |
| Learning Diary | 0 | 0 | 0 |
| Thesis/ Project | 0 | 0 | 0 |
| Seminar | 0 | 0 | 0 |
| Other | 0 | 0 | 0 |
| Make-up | 0 | 0 | 0 |
| Yıl Sonu | 0 | 0 | 0 |
| Hazırlık Yıl Sonu | 0 | 0 | 0 |
| Total Workload | 196 | ||
| Total Workload / 25 | 7.84 | ||
| Credits ECTS | 8 | ||