Teaching
I have extensive experience in teaching and student mentoring at the university level, progressing from teaching assistant roles to instructor of record positions. My teaching spans applied mathematics, scientific computing, and physics-based modeling across multiple institutions. Throughout my career, I have consistently employed interactive teaching methods, emphasizing active learning and student engagement through innovative pedagogical approaches including flipped classroom techniques. My experience encompasses leading lectures, coordinating project work, mentoring undergraduate and graduate research, and developing comprehensive educational materials. Below is a detailed overview of courses I taught with a more detailed breakdown of each course's content, my role, and teaching approach.
University of Notre Dame
As a postdoctoral researcher at the University of Notre Dame, I serve as a co-mentor for several undergraduate and graduate students, guiding them through research projects in applied scientific computing and engineering. My mentoring approach combines theoretical foundations with practical applications, helping students develop both analytical skills and computational expertise. A comprehensive list of current and completed projects will be added to this website soon.
Students Advised
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TBD
University of Tennessee, Knoxville
During my time at the University of Tennessee, Knoxville, I served as instructor of record and in co-teaching roles, taking full responsibility for course delivery. This included holding lectures, creating and grading quizzes and exams, maintaining office hours, and developing curriculum materials. My classroom approach emphasizes interactive learning, incorporating active learning techniques and occasionally implementing flipped classroom methodologies to enhance student engagement and comprehension.
Courses Taught
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Spring 2023 – Finite Math (MTH 123)
Finite Math (MTH 123)
University of Tennessee, Knoxville, Spring 2023
Role and Teaching Approach
As instructor of record, I was responsible for all aspects of the course including holding lectures, maintaining office hours, planning curriculum, and creating and grading all exams, quizzes, and syllabus materials. I implemented many active learning and flipped classroom techniques, and my students consistently performed above average compared to other sections.
Course Overview
This course introduces mathematical concepts and techniques used in business and social sciences. The emphasis is on practical applications of finite mathematics including linear algebra, linear programming, and game theory, with particular focus on financial mathematics and decision-making strategies.
Learning Objectives
Upon completion of Math 123, students are able to:
- Use correct mathematical language and notation
- Solve real-world financial problems (including investments, annuities, and loans) by determining and using appropriate methods
- Solve systems of linear equations using appropriate methods (including graphing, algebraic elimination, matrix row reduction and matrix inversion)
- Perform matrix operations by hand
- Solve linear programming problems using appropriate methods (including graphing and the simplex method)
- Set up and interpret payoff matrices and strategy matrices for two-person, zero-sum games
- Apply game theory techniques to determine optimal strategies and the expected value of a game
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Fall 2022 – Finite Math (MTH 123)
Finite Math (MTH 123)
University of Tennessee, Knoxville, Fall 2022
Role and Teaching Approach
As instructor of record, I was responsible for all aspects of the course including holding lectures, maintaining office hours, planning curriculum, and creating and grading all exams, quizzes, and syllabus materials. I implemented many active learning and flipped classroom techniques, and my students consistently performed above average compared to other sections.
Course Overview
This course introduces mathematical concepts and techniques used in business and social sciences. The emphasis is on practical applications of finite mathematics including linear algebra, linear programming, and game theory, with particular focus on financial mathematics and decision-making strategies.
Learning Objectives
Upon completion of Math 123, students are able to:
- Use correct mathematical language and notation
- Solve real-world financial problems (including investments, annuities, and loans) by determining and using appropriate methods
- Solve systems of linear equations using appropriate methods (including graphing, algebraic elimination, matrix row reduction and matrix inversion)
- Perform matrix operations by hand
- Solve linear programming problems using appropriate methods (including graphing and the simplex method)
- Set up and interpret payoff matrices and strategy matrices for two-person, zero-sum games
- Apply game theory techniques to determine optimal strategies and the expected value of a game
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Spring 2022 – Basic Calculus (MTH 125)
Basic Calculus (MTH 125)
University of Tennessee, Knoxville, Spring 2022
Role and Teaching Approach
As instructor of record, I was responsible for all aspects of the course including holding lectures, maintaining office hours, planning curriculum, and creating and grading all exams, quizzes, and syllabus materials. I implemented many active learning and flipped classroom techniques, and my students consistently performed above average compared to other sections.
Course Overview
This course introduces fundamental concepts of differential and integral calculus, designed for students who need calculus for applications but are not pursuing mathematics degrees. The emphasis is on practical problem-solving and real-world applications rather than theoretical rigor.
Learning Objectives
Upon completion of Math 125, students are able to:
- Evaluate limits numerically, algebraically and graphically
- Describe the discontinuities and intervals of continuity of a function
- Use the slope of the secant line and average rate of change to approximate the value of the derivative
- Interpret the derivative, using limits, as the slope of the tangent line and instantaneous rate of change
- Apply derivative rules (power, product, quotient and chain rules) to algebraic, exponential, and logarithmic functions
- Use derivatives to solve physical and economic optimization problems
- Use the first and second derivatives to determine the intervals on which a function is increasing and decreasing, relative and absolute extrema, and intervals of concavity and inflection points of a function
- Apply integration rules to find indefinite integrals of algebraic, exponential, and logarithmic functions (including composite functions)
- Use rectangles to approximate the value of the definite integral
- Interpret the definite integral as the area under the curve
- Evaluate definite integrals of algebraic, exponential, and logarithmic functions (including composite functions) using the Fundamental Theorem of Calculus
- Use definite integrals to find the area bounded by the x-axis and the graph of a function, the area between the graphs of two functions, and the average value of a function
- Determine the appropriate calculus technique needed to solve real world problems
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Fall 2021 – Basic Calculus (MTH 125)
Basic Calculus (MTH 125)
University of Tennessee, Knoxville, Fall 2021
Role and Teaching Approach
As instructor of record, I was responsible for all aspects of the course including holding lectures, maintaining office hours, planning curriculum, and creating and grading all exams, quizzes, and syllabus materials. I implemented many active learning and flipped classroom techniques, and my students consistently performed above average compared to other sections.
Course Overview
This course introduces fundamental concepts of differential and integral calculus, designed for students who need calculus for applications but are not pursuing mathematics degrees. The emphasis is on practical problem-solving and real-world applications rather than theoretical rigor.
Learning Objectives
Upon completion of Math 125, students are able to:
- Evaluate limits numerically, algebraically and graphically
- Describe the discontinuities and intervals of continuity of a function
- Use the slope of the secant line and average rate of change to approximate the value of the derivative
- Interpret the derivative, using limits, as the slope of the tangent line and instantaneous rate of change
- Apply derivative rules (power, product, quotient and chain rules) to algebraic, exponential, and logarithmic functions
- Use derivatives to solve physical and economic optimization problems
- Use the first and second derivatives to determine the intervals on which a function is increasing and decreasing, relative and absolute extrema, and intervals of concavity and inflection points of a function
- Apply integration rules to find indefinite integrals of algebraic, exponential, and logarithmic functions (including composite functions)
- Use rectangles to approximate the value of the definite integral
- Interpret the definite integral as the area under the curve
- Evaluate definite integrals of algebraic, exponential, and logarithmic functions (including composite functions) using the Fundamental Theorem of Calculus
- Use definite integrals to find the area bounded by the x-axis and the graph of a function, the area between the graphs of two functions, and the average value of a function
- Determine the appropriate calculus technique needed to solve real world problems
Oregon State University
As a PhD student at Oregon State University, I was responsible for running courses in the Mathematics Department. My duties included conducting recitation sessions, grading and presenting homework and exam solutions, and delivering lectures as a substitute instructor or in co-teaching arrangements. I maintained interactive classrooms using active learning approaches, occasionally implementing flipped classroom techniques to maximize student participation and understanding. Due to COVID-19, several courses were delivered remotely, requiring adaptation of pedagogical methods to online formats while maintaining student engagement.
Courses Taught
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Spring 2021 – Advanced Calculus II (MTH 312)
Advanced Calculus II (MTH 312)
Oregon State University, Spring 2021
Role and Teaching Approach
I conducted recitation sessions for the lecture course taught by Prof. Dr. Radu Dascaliuc. Due to COVID-19, all sessions continued to be delivered remotely, building upon the proof-based foundation established in MTH 311 while advancing students' theoretical understanding and analytical skills.
Course Overview
This course continues the rigorous development of calculus begun in MTH 311, serving as the second part of the proof-based analysis sequence. Students deepen their understanding of real analysis while developing advanced proof techniques and mathematical maturity essential for upper-level mathematics courses.
Topics Covered
- Advanced properties of real numbers and completeness
- Deeper topology of the real line
- Advanced convergence theory for sequences and series
- Detailed function theory and continuity
- Advanced derivative properties and applications
- Comprehensive Riemann integration theory
- Advanced treatment of improper integrals
- Detailed sequences of functions analysis
- Uniform convergence and its applications
- Extended multivariable calculus foundations
Learning Objectives
Students advance their ability to:
- Construct sophisticated mathematical proofs and counterexamples
- Master advanced epsilon-delta techniques
- Understand deep connections between analysis concepts
- Analyze complex convergence and continuity problems
- Apply theoretical results to solve advanced problems
- Develop mathematical maturity for graduate-level mathematics
Teaching Methods
Recitation sessions emphasized advanced proof techniques and mathematical reasoning, helping students master sophisticated analytical arguments. Through remote platforms, I facilitated collaborative proof development, guided students through complex theoretical problems, and provided individualized feedback on advanced mathematical communication and proof-writing skills.
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Winter 2021 – Advanced Calculus I (MTH 311)
Advanced Calculus I (MTH 311)
Oregon State University, Winter 2021
Role and Teaching Approach
I conducted recitation sessions for the lecture course taught by Prof. Dr. Patrick De Leenheer. Due to COVID-19, all sessions were delivered remotely, requiring adaptation of proof-based instruction to online formats while helping students develop mathematical rigor and proof-writing skills.
Course Overview
This course provides a rigorous development of calculus and serves as one of the first proof-based courses for most mathematics students. The course establishes the theoretical foundations of calculus through careful axiomatization and logical development, emphasizing mathematical reasoning and formal proof techniques.
Topics Covered
- Axiomatic properties of the real numbers
- Topology of the real line
- Convergence of sequences and series of real numbers
- Functions and limits of functions
- Basic properties of continuity and derivatives
- Riemann integration theory
- Improper integrals
- Sequences of functions
- Pointwise and uniform convergence
- Introductory multivariable calculus concepts
Learning Objectives
Students develop skills to:
- Construct rigorous mathematical proofs
- Work with epsilon-delta definitions of limits and continuity
- Understand the theoretical foundations of calculus
- Analyze convergence properties of sequences and series
- Apply formal definitions to prove fundamental calculus theorems
- Transition from computational to theoretical mathematics
Teaching Methods
Recitation sessions focused on proof development and mathematical communication, helping students master the transition from computational calculus to rigorous analysis. Through online platforms, I guided students through proof construction, provided feedback on mathematical writing, and facilitated discussions about theoretical concepts in a remote learning environment.
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Fall 2020 – Linear Algebra II (MTH 342)
Linear Algebra II (MTH 342)
Oregon State University, Fall 2020
Role and Teaching Approach
I conducted recitation sessions for the lecture course taught by Prof. Dr. Patrick De Leenheer. Due to COVID-19, all sessions were delivered remotely, requiring innovative approaches to facilitate student understanding of abstract mathematical concepts and proof techniques in an online environment.
Course Overview
This advanced linear algebra course is proof-based, focusing on the theoretical foundations and abstract structures of linear algebra. Building upon the computational skills from MTH 341, students develop mathematical rigor and learn to work with abstract vector spaces over real and complex fields.
Topics Covered
- Abstract vector spaces (real and complex)
- Linear transformations and their properties
- Inner product spaces and orthogonality
- Eigenspaces and diagonalization theory
- Spectral theorems and applications
- Singular value decomposition
- Canonical forms and structure theorems
- Advanced applications to geometry and analysis
Learning Objectives
Students develop theoretical understanding to:
- Construct rigorous proofs in linear algebra contexts
- Work with abstract vector spaces and linear transformations
- Apply spectral theory to diagonalization problems
- Understand and utilize inner product structures
- Analyze eigenspaces and their geometric properties
- Connect linear algebra theory to broader mathematical concepts
Teaching Methods
Recitation sessions focused on proof development and mathematical reasoning, helping students transition from computational to theoretical approaches. Through online platforms, I facilitated collaborative proof construction, guided students through complex theoretical problems, and provided individualized support for developing mathematical communication skills in the remote learning environment.
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Spring 2020 – Linear Algebra I (MTH 341)
Linear Algebra I (MTH 341)
Oregon State University, Spring 2020
Role and Teaching Approach
I served as co-instructor as part of a collaborative teaching team consisting of three instructors and two undergraduate assistants. Due to COVID-19, this course was delivered entirely online, requiring adaptation of traditional linear algebra instruction to remote learning formats while maintaining student engagement and computational skill development.
Course Overview
This introductory linear algebra course is computation-focused, providing students with foundational skills in matrix operations and linear systems. The course emphasizes practical problem-solving techniques and algorithmic approaches to linear algebra concepts, preparing students for applications in engineering, mathematics, and related fields.
Topics Covered
- Matrix algebra and operations
- Determinants and their properties
- Systems of linear equations and solution methods
- Vector spaces and subspaces
- Introductory eigenvalues and eigenvectors
- Row reduction and Gaussian elimination
- Matrix inverses and applications
- Linear independence and span
Learning Objectives
Students develop computational skills to:
- Perform matrix operations efficiently and accurately
- Solve systems of linear equations using multiple methods
- Calculate determinants and understand their geometric significance
- Identify and work with vector subspaces
- Compute basic eigenvalues and eigenvectors
- Apply linear algebra techniques to real-world problems
Teaching Methods
The course adapted traditional computational instruction to online formats, emphasizing interactive problem-solving sessions and collaborative learning among the teaching team. We developed strategies to maintain student engagement through virtual office hours, online computational exercises, and coordinated instruction across multiple sections.
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Winter 2020 – College Algebra (MTH 111)
College Algebra (MTH 111)
Oregon State University, Winter 2020
Role and Teaching Approach
I served as co-instructor alongside Amanda Blaisdale (instructor of record), delivering one of four weekly lectures to classes of approximately 120 students. My responsibilities included coordinating three undergraduate teaching assistants during interactive and group work portions of lectures, implementing active learning techniques in large classroom settings.
Course Overview
This course focuses on the study of functions and their properties using a Function Family Approach. Students develop mathematical models for real-world situations using seven function families, emphasizing connections between function properties and their applications. The course satisfies Oregon State University's Baccalaureate Core Mathematics requirement.
Function Families Covered
- Polynomial (including Linear and Quadratic)
- Radical functions
- Piecewise functions
- Absolute value functions
- Rational functions
- Exponential functions
- Logarithmic functions
Learning Objectives
Students learn to:
- Analyze functions using multiple representations (symbolic, numerical, graphical, verbal)
- Build new functions from ten basic parent functions through transformations
- Identify and model real-world situations mathematically
- Determine function properties: domain/range, intercepts, asymptotes, end behavior
- Apply mathematical reasoning and problem-solving strategies
- Choose appropriate function models for given contexts
Teaching Methods
The course emphasized team-based learning with structured activities including warm-ups, collaborative lessons, and wrap-up assessments. Students worked in teams to solve problems, build mathematical understanding, and develop communication skills through interactive classroom engagement.
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Fall 2019 – Elementary Functions (MTH 112)
Elementary Functions - Precalculus II: Trigonometry (MTH 112Z)
Oregon State University, Fall 2019
Role and Teaching Approach
I conducted recitation sessions for approximately 120 students total, working under the supervision of Dr. Johnner Barrett. Together, we designed innovative course materials intended for use in future iterations of the course. My responsibilities included leading smaller discussion sections, facilitating problem-solving activities, and implementing active learning techniques in precalculus education.
Course Overview
This course serves as Precalculus II, designed for students preparing for calculus and related disciplines. The focus is on trigonometric functions and their applications, building upon the function family approach established in MTH 111. The course satisfies Oregon State University's Baccalaureate Core Mathematics requirement for Quantitative Literacy & Analysis.
Topics Covered
- Angle measurement and properties (degrees and radians)
- Unit circle and trigonometric identities
- Trigonometric functions: sine, cosine, tangent and their inverses
- Transformations of trigonometric functions
- Triangle trigonometry and applications
- Periodic functions and their modeling applications
- Vector operations and applications
- Polar coordinates and complex numbers
Learning Objectives
Students develop skills to:
- Analyze trigonometric functions using multiple representations (symbolic, numerical, graphical)
- Apply trigonometric concepts to real-world modeling problems
- Solve triangles using trigonometric ratios and laws
- Work with vectors in geometric and applied contexts
- Use technology appropriately for trigonometric calculations and graphing
- Connect trigonometric concepts with other mathematical disciplines
Teaching Methods
The course emphasized multiple representations of trigonometric concepts, exploring topics symbolically, numerically, and graphically through real-life applications. Working with Dr. Barrett, we developed materials that emphasized skill building, problem solving, mathematical modeling, and communication skills. The course incorporated appropriate use of present-day technology for visualization and computation.
University of Konstanz
During my Bachelor's and Master's studies at the University of Konstanz, I was hired as a teaching assistant across multiple departments: Mathematics, Computer Science, and Physics. I taught both mathematics and theoretical physics courses, with responsibilities including grading and presenting homework and exam solutions, conducting weekly recitation sessions, and maintaining regular office hours for student support. My teaching approach emphasized interactive learning through active learning techniques, creating engaging educational experiences across diverse mathematical and scientific disciplines.
Courses Taught
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Summer 2019 – Real Analysis II
Analysis II (Teaching Assistant)
University of Konstanz, Summer 2019
Course Overview
This proof-based course (taught in German) is an obligatory part of the mathematics bachelor curriculum and is also frequently attended by interested students from physics and computer science. The course, taught by Prof. Dr. Heinrich Freistühler, built on Analysis I and introduced advanced concepts in real and functional analysis, including:
Topics Covered
- Differentiability in several variables, local invertibility, Banach's fixed-point theorem, and the implicit function theorem.
- Constrained extrema and the method of Lagrange multipliers.
- Multidimensional integration and the divergence theorem (Gauss's theorem).
- Continuity in several variables and in metric spaces.
- Metric spaces: connectedness, product spaces, compactness.
- Riemann integration, interchange of limits and integrals, change of variables formula.
- Taylor series expansions and convergence.
- Foundations: sets, mappings, logic, and cardinality.
- Number systems: real and complex numbers.
- Sequences, series, power series, and uniform convergence.
Teaching Duties
- Conducted weekly recitation sessions to review material and practice proofs.
- Prepared and presented detailed solutions to homework assignments.
- Graded homework as well as final examinations.
- Provided individual support to students during office hours.
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Summer 2019 – Linear Algebra and Analysis for Computer Scientists
Linear Algebra and Analysis for Computer Scientists (Teaching Assistant)
University of Konstanz, Summer 2019
Course Overview
This proof-based course (taught in German) is an obligatory part of the computer science bachelor curriculum. The course, taught by Prof. Dr. Sven Kosub, introduces continuous mathematical methods essential for computer science, with a focus on uncountable sets and structures, particularly real-valued functions. While maintaining mathematical rigor, the course is tailored specifically for CS students rather than pure mathematics.
The goal is to develop both conceptual and operational understanding of analytical, linear algebraic, and vector analytical concepts and techniques relevant to computer science.
Topics Covered
- Sequences and series
- Differential calculus
- Integral calculus
- Power series
- Linear spaces
- Linear mappings
- Eigenspaces
- Vector analysis
Teaching Duties
- Conducted weekly recitation sessions focusing on computational techniques and CS applications.
- Prepared and presented detailed solutions to homework assignments with emphasis on algorithmic thinking.
- Graded homework and examinations.
- Provided individual support to students during office hours, helping bridge mathematical concepts with computer science applications.
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Winter 2018/19 – Theoretical Physics III
Theoretical Physics III (Teaching Assistant)
University of Konstanz, Winter 2018/19
Course Overview
This course is the theoretical component of an integrated introduction to physics that combines experimental and theoretical physics in a complementary manner. Taught by Prof. Dr. Peter Nielaba, this is the third semester of a four-semester sequence that provides a comprehensive foundation in theoretical physics for physics majors.
The course covers advanced topics in optics, special relativity, thermodynamics, and analytical mechanics, building upon the foundations established in Theoretical Physics I and II. The integration with experimental physics ensures that students develop both theoretical understanding and practical intuition for physical phenomena.
Topics Covered
Optics (Optik):
- Light as electromagnetic waves
- Polarization phenomena
- Classical models of light-matter interaction
- Refractive index and dispersion
- Geometric optics and ray tracing
- Wave optics: interference, diffraction, and scattering
Special Relativity (Spezielle Relativitätstheorie):
- Principle of relativity and Lorentz transformations
- Einstein's equations of motion
- Relativistic kinematics and dynamics
- Space-time geometry and four-vectors
Thermodynamics (Thermodynamik):
- Fundamental thermodynamic quantities: energy, entropy, temperature, pressure, volume, particle number, chemical potential
- Experimental determination of thermodynamic properties
- Ideal and real gases
- Thermal properties of matter
- Laws of thermodynamics
- Entropy and irreversibility
- Formal aspects of thermodynamics
- Phase transitions and critical phenomena
Analytical Mechanics (Analytische Mechanik):
- Lagrangian formulation of mechanics
- Hamiltonian formulation of mechanics
- Variational problems and calculus of variations
- Symmetries and conservation laws
- Perturbation theory and approximation methods
Teaching Duties
- Conducted weekly recitation sessions to work through problem sets and theoretical derivations.
- Prepared and presented detailed solutions to homework assignments.
- Graded homework and examinations.
- Provided individual support to students during office hours, helping connect theoretical concepts with experimental observations.
- Assisted students in developing problem-solving strategies for complex multi-step physics problems.
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Winter 2018/19 – Mathematics for Physicists III
Mathematics for Physicists III (Teaching Assistant)
University of Konstanz, Winter 2018/19
Course Overview
This proof-based course (taught in German) is part of the mathematics sequence for physics students at the University of Konstanz, taught by Prof. Dr. Markus Kunze. The course is offered as an alternative to attending the pure mathematicians' real analysis and linear algebra sequences, specifically tailored for physics students while maintaining mathematical rigor.
The lecture consists of two main areas: Ordinary Differential Equations and Complex Analysis (Funktionentheorie). For ordinary differential equations, important solvability results (e.g., Picard-Lindelöf theorem) as well as solution methods are discussed. In complex analysis, holomorphic functions of one variable are studied and central properties and results of this beautiful theory are presented.
This is the third and final course in the series, building on the foundations established in Mathematics for Physicists I and II. The course provides essential mathematical tools for advanced physics, particularly in quantum mechanics, electrodynamics, and theoretical physics.
Topics Covered
Ordinary Differential Equations:
- Phase portraits
- Elementary solution methods
- Simple numerical methods
- General existence statements
- Linear differential equations and systems
- Fundamental systems, Wronskian determinants
- Systems with constant coefficients
- Boundary and eigenvalue problems for formally self-adjoint operators
Complex Analysis (Funktionentheorie):
- Complex differentiability
- Cauchy-Riemann differential equations and harmonic functions
- Complex logarithm
- Complex line integrals
- Cauchy's integral theorem and integral formula
- Power series representation of holomorphic functions
- Liouville's theorem
- Residue theorem and Laurent series
Teaching Duties
- Conducted weekly recitation sessions to review material and practice proofs.
- Prepared and presented detailed solutions to homework assignments.
- Graded homework as well as final examinations.
- Provided individual support to students during office hours.
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Summer 2018 – Discrete Mathematics
Discrete Mathematics (Teaching Assistant)
University of Konstanz, Summer 2018
Course Overview
This proof-based course (taught in German) is an obligatory part of the computer science bachelor curriculum at the University of Konstanz, taught by Prof. Dr. Sven Kosub. The course introduces computer science students to fundamental mathematical concepts and techniques that are essential for their field, emphasizing discrete structures and combinatorial reasoning.
The course covers mathematical foundations crucial for algorithm analysis, data structures, and theoretical computer science, providing students with the mathematical toolkit necessary for advanced CS coursework.
Topics Covered
Basic Group Theory:
- Group axioms and basic properties
- Examples of groups relevant to computer science
- Applications to cryptography and coding theory
Combinatorics:
- Basic principles: sum rule, product rule
- Permutations & combinations with/without repetition
- Binomial theorem and combinatorial proofs
- Inclusion-exclusion principle
- Pigeonhole principle and applications
- Counting subsets, partitions, and derangements
Graph Theory:
- Basic definitions: vertices, edges, degree, adjacency
- Graph types: simple, multigraphs, bipartite, complete, trees
- Connectedness, paths, cycles, Eulerian and Hamiltonian paths
- Planar graphs and Euler's formula
- Graph representations: adjacency matrix, adjacency list
- Applications: shortest paths, spanning trees, network flows
Recurrence Relations:
- Linear recurrences with constant coefficients
- Non-homogeneous recurrences and particular solutions
- Divide-and-conquer recurrences and Master Theorem
- Applications: Fibonacci numbers, algorithm analysis
Generating Functions:
- Ordinary and exponential generating functions
- Operations: shifting, convolution, differentiation
- Solving recurrence relations
- Counting problems and binomial identities
Teaching Duties
- Conducted weekly recitation sessions to review material and practice proofs.
- Prepared and presented detailed solutions to homework assignments.
- Graded homework as well as final examinations.
- Provided individual support to students during office hours.
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Summer 2018 – Mathematics for Physicists II
Mathematics for Physicists II (Teaching Assistant)
University of Konstanz, Summer 2018
Course Overview
This proof-based course (taught in German) is part of the mathematics sequence for physics students at the University of Konstanz, taught by Prof. Dr. Markus Kunze. The course is offered as an alternative to attending the pure mathematicians' real analysis and linear algebra sequences, specifically tailored for physics students while maintaining mathematical rigor.
This is the second course in the series, building on Mathematics for Physicists I and serving as preparation for Mathematics for Physicists III. The course covers advanced topics in multivariable calculus, linear algebra, and integration theory essential for physics applications.
Topics Covered
Multivariable Calculus:
- Differentiation in R^n: partial derivatives, gradients, and chain rule
- Higher-order derivatives and differential operators
- Vector analysis: divergence, curl, and Laplacian
- Inverse and implicit function theorems
- Constrained optimization and Lagrange multipliers
- Legendre transforms (applications to mechanics and thermodynamics)
Linear Algebra:
- Determinants and their properties
- Applications to linear systems and Cramer's rule
- Eigenvalues and eigenvectors
- Jordan normal form
- Quadratic forms and matrix definiteness
Integration and Geometry:
- Integration techniques: partial integration, substitution, partial fractions
- Fourier series and convergence theory
- Curve theory and parametric representations
- Line integrals (first and second kind)
- Surface integrals and multidimensional integration
- Integral theorems: Green's, Gauss's, and Stokes' theorems
Teaching Duties
- Conducted weekly recitation sessions to review material and practice proofs.
- Prepared and presented detailed solutions to homework assignments.
- Graded homework as well as final examinations.
- Provided individual support to students during office hours.
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Winter 2017/18 – Mathematics for Physicists III
Mathematics for Physicists III (Teaching Assistant)
University of Konstanz, Winter 2017/18
Course Overview
This proof-based course (taught in German) is part of the mathematics sequence for physics students at the University of Konstanz, taught by Prof. Dr. Markus Kunze. The course is offered as an alternative to attending the pure mathematicians' real analysis and linear algebra sequences, specifically tailored for physics students while maintaining mathematical rigor.
The lecture consists of two main areas: Ordinary Differential Equations and Complex Analysis (Funktionentheorie). For ordinary differential equations, important solvability results (e.g., Picard-Lindelöf theorem) as well as solution methods are discussed. In complex analysis, holomorphic functions of one variable are studied and central properties and results of this beautiful theory are presented.
This is the third and final course in the series, building on the foundations established in Mathematics for Physicists I and II. The course provides essential mathematical tools for advanced physics, particularly in quantum mechanics, electrodynamics, and theoretical physics.
Topics Covered
Ordinary Differential Equations:
- Phase portraits
- Elementary solution methods
- Simple numerical methods
- General existence statements
- Linear differential equations and systems
- Fundamental systems, Wronskian determinants
- Systems with constant coefficients
- Boundary and eigenvalue problems for formally self-adjoint operators
Complex Analysis (Funktionentheorie):
- Complex differentiability
- Cauchy-Riemann differential equations and harmonic functions
- Complex logarithm
- Complex line integrals
- Cauchy's integral theorem and integral formula
- Power series representation of holomorphic functions
- Liouville's theorem
- Residue theorem and Laurent series
Teaching Duties
- Conducted weekly recitation sessions to review material and practice proofs.
- Prepared and presented detailed solutions to homework assignments.
- Graded homework as well as final examinations.
- Provided individual support to students during office hours.
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Summer 2017 – Mathematics for Physicists II
Mathematics for Physicists II (Teaching Assistant)
University of Konstanz, Summer 2017
Course Overview
This proof-based course (taught in German) is part of the mathematics sequence for physics students at the University of Konstanz, taught by Prof. Dr. Markus Kunze. The course is offered as an alternative to attending the pure mathematicians' real analysis and linear algebra sequences, specifically tailored for physics students while maintaining mathematical rigor.
This is the second course in the series, building on Mathematics for Physicists I and serving as preparation for Mathematics for Physicists III. The course covers advanced topics in multivariable calculus, linear algebra, and integration theory essential for physics applications.
Topics Covered
Multivariable Calculus:
- Differentiation in R^n: partial derivatives, gradients, and chain rule
- Higher-order derivatives and differential operators
- Vector analysis: divergence, curl, and Laplacian
- Inverse and implicit function theorems
- Constrained optimization and Lagrange multipliers
- Legendre transforms (applications to mechanics and thermodynamics)
Linear Algebra:
- Determinants and their properties
- Applications to linear systems and Cramer's rule
- Eigenvalues and eigenvectors
- Jordan normal form
- Quadratic forms and matrix definiteness
Integration and Geometry:
- Integration techniques: partial integration, substitution, partial fractions
- Fourier series and convergence theory
- Curve theory and parametric representations
- Line integrals (first and second kind)
- Surface integrals and multidimensional integration
- Integral theorems: Green's, Gauss's, and Stokes' theorems
Teaching Duties
- Conducted weekly recitation sessions to review material and practice proofs.
- Prepared and presented detailed solutions to homework assignments.
- Graded homework as well as final examinations.
- Provided individual support to students during office hours.
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Winter 2016/17 – Mathematics for Physicists I
Mathematics for Physicists I (Teaching Assistant)
University of Konstanz, Winter 2016/17
Course Overview
This proof-based course (taught in German) is the foundational course in the mathematics sequence for physics students at the University of Konstanz, taught by Prof. Dr. Markus Kunze. The course is offered as an alternative to attending the pure mathematicians' real analysis and linear algebra sequences, specifically tailored for physics students while maintaining mathematical rigor.
This is the first course in the three-part series, establishing essential mathematical foundations for advanced physics studies. The course covers fundamental concepts in analysis, linear algebra, and complex numbers that serve as prerequisites for Mathematics for Physicists II and III.
Topics Covered
Number Systems and Complex Analysis Foundations:
- Real numbers and elementary functions
- Complex numbers: arithmetic, polar form, and applications
- Functions of complex variables
- Applications to electrical engineering and mechanics
Vector Spaces and Linear Algebra:
- R² and R³: geometric properties and rotations
- Group theory fundamentals and applications to physics
- Vector spaces: linear independence, bases, and dimension
- Inner products, norms, and orthogonal systems
- Matrix operations and linear equation systems
- Linear transformations and homomorphisms
Analysis Foundations:
- Sequences and series in normed spaces
- Convergence criteria and completeness
- Power series and radius of convergence
- Exponential function and elementary functions
- Limits, continuity, and differentiability
- Mean value theorem and Taylor's theorem
- Trigonometric and hyperbolic functions
- Numerical methods: bisection, Newton's method, fixed-point iteration
Teaching Duties
- Conducted weekly recitation sessions to review material and practice proofs.
- Prepared and presented detailed solutions to homework assignments.
- Graded homework as well as final examinations.
- Provided individual support to students during office hours.
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Summer 2016 – Discrete Mathematics
Discrete Mathematics (Teaching Assistant)
University of Konstanz, Summer 2016
Course Overview
This proof-based course (taught in German) is an obligatory part of the computer science bachelor curriculum at the University of Konstanz, taught by Prof. Dr. Sven Kosub. The course introduces computer science students to fundamental mathematical concepts and techniques that are essential for their field, emphasizing discrete structures and combinatorial reasoning.
The course covers mathematical foundations crucial for algorithm analysis, data structures, and theoretical computer science, providing students with the mathematical toolkit necessary for advanced CS coursework.
Topics Covered
Basic Group Theory:
- Group axioms and basic properties
- Examples of groups relevant to computer science
- Applications to cryptography and coding theory
Combinatorics:
- Basic principles: sum rule, product rule
- Permutations & combinations with/without repetition
- Binomial theorem and combinatorial proofs
- Inclusion-exclusion principle
- Pigeonhole principle and applications
- Counting subsets, partitions, and derangements
Graph Theory:
- Basic definitions: vertices, edges, degree, adjacency
- Graph types: simple, multigraphs, bipartite, complete, trees
- Connectedness, paths, cycles, Eulerian and Hamiltonian paths
- Planar graphs and Euler's formula
- Graph representations: adjacency matrix, adjacency list
- Applications: shortest paths, spanning trees, network flows
Recurrence Relations:
- Linear recurrences with constant coefficients
- Non-homogeneous recurrences and particular solutions
- Divide-and-conquer recurrences and Master Theorem
- Applications: Fibonacci numbers, algorithm analysis
Generating Functions:
- Ordinary and exponential generating functions
- Operations: shifting, convolution, differentiation
- Solving recurrence relations
- Counting problems and binomial identities
Teaching Duties
- Conducted weekly recitation sessions to review material and practice proofs.
- Prepared and presented detailed solutions to homework assignments.
- Graded homework as well as final examinations.
- Provided individual support to students during office hours.