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- MTH424: Convex Analysis (Spring 2024)
- vex hull and their properties, Best approximation theorem. Convex functions, Basic definitions, properties,
- MTH103: Exploring Quantitative Skills
- amentals of Geometry, Applications of Pythagorean theorem, Introduction to unit circles, trigonometric func
- MTH322: Real Analysis II (Spring 2023)
- functions, radius of convergence, Cauchy-Hadamard theorem, differentiation theorem, uniqueness theorem. **Improper integrals:** Improper integral of first and second kind, comparison tests
- MTH321: Real Analysis I (Spring 2023)
- accumulation point, prove the Bolzano-Weierstrass theorem, Rolles’s Theorem, extreme value theorem, and the Mean Value theorem and emphasize the proofs’ development. Define Riemann integral and Riemann sum
- MTH321: Real Analysis I (Fall 2022)
- accumulation point, prove the Bolzano-Weierstrass theorem, Rolles’s Theorem, extreme value theorem, and the Mean Value theorem and emphasize the proofs’ development. Define Riemann integral and Riemann sum
- MTH604: Fixed Point Theory and Applications (Fall 2022)
- focus on Banach Fixed Point theorems fixed point theorem and its application to nonlinear differential equ... Kannan Fixed Point theorems, Banach Fixed Point theorem for multi-valued mappings are also educated. ==... ample questions===== - State intermediate value theorem. - State and prove the fixed point theorem. - Define attracting, repelling and neutral fixed points.
- MTH321: Real Analysis I (Fall 2021)
- accumulation point, prove the Bolzano-Weierstrass theorem, Rolles’s Theorem, extreme value theorem, and the Mean Value theorem and emphasize the proofs’ development. Define Riemann integral and Riemann sum
- MTH251: Set Topology
- y continuous mappings. Pseudometrics. Fixed point theorem for metric spaces; Topological Spaces. Open bases... ces, Urysohn's Lemma; Compact spaces, Tychonoff's theorem and locall compact spaces, Compactness for Metric
- MTH322: Real Analysis II (Spring 2022)
- functions, radius of convergence, Cauchy-Hadamard theorem, differentiation theorem, uniqueness theorem. **Improper integrals:** Improper integral of first and second kind, comparison tests
- MTH322: Real Analysis II (Fall 2021)
- functions, radius of convergence, Cauchy-Hadamard theorem, differentiation theorem, uniqueness theorem. **Improper integrals:** Improper integral of first and second kind, comparison tests... (x)dx}$ is convergent. - State and prove Abel's theorem for infinite integral. - If $f(x)$ is bounded,
- MTH604: Fixed Point Theory and Applications (Spring 2021)
- focus on Banach Fixed Point theorems fixed point theorem and its application to nonlinear differential equ... Kannan Fixed Point theorems, Banach Fixed Point theorem for multi-valued mappings are also educated. ==... xed point. - State and prove intermediate value theorem. - State and prove the fixed point theorem. - Define attracting, repelling and neutral fixed point the
- MTH321: Real Analysis I (Spring 2020)
- accumulation point, prove the Bolzano-Weierstrass theorem, Rolles’s Theorem, extreme value theorem, and the Mean Value theorem and emphasize the proofs’ development. Define Riemann integral and Riemann sum
- MTH604: Fixed Point Theory and Applications (Spring 2020)
- focus on Banach Fixed Point theorems fixed point theorem and its application to nonlinear differential equ... Kannan Fixed Point theorems, Banach Fixed Point theorem for multi-valued mappings are also educated. ==... tions===== - State and prove intermediate value theorem. - State and prove the fixed point theorem. - Define attracting, repelling and neutral fixed point the
- MTH633: Advanced Convex Analysis (Spring 2019)
- paration theorems, hyperplane, Best approximation theorem and its applications, Farkas and Gordan Theorems,
- MTH322: Real Analysis II (Spring 2019)
- functions, radius of convergence, Cauchy-Hadamard theorem, differentiation theorem, uniqueness theorem. **Improper integrals:** Improper integral of first and second kind, comparison tests