Simon
H. Hvidtfeldt
University Student: Machine Learning and Data Science
University Education
Bachelor in Machine Learning & Data Science
University of Copenhagen | 2024 - Present
About the course: Introduction to Python, control structures, and problem-solving.
Knowledge of
- Basic concepts within imperative, object-oriented, and functional programming.
- Control structures, loops, classes, objects, inheritance, and recursion.
- Good programming practices: Documentation, design patterns, and unit testing.
- Technical analysis of natural language problems.
Skills in
- Reading and writing programs (up to approx. 1000 lines) while adhering to good practices.
- Evaluating advantages and disadvantages of different solution models.
- Implementing, testing, and documenting the quality of the solution.
- Applying appropriate study techniques to ensure progress.
Competences to
- Analyze problems based on a precise problem statement.
- Design and program solutions to the given problem.
- Verify, test, and document the final solution.
About the course: Basic mathematical tools and methods with a focus on scientific application.
Knowledge of
- Understanding of elementary aspects of mathematical subjects and theories.
- Mastery of mathematical concepts to a degree that enables application in further studies.
Skills in
- Perform differentiation, integration, and extrema investigations of functions of 1 and multiple variables.
- Solve typical 1st and 2nd order differential equations.
- Determine limits, convergence, and Taylor polynomials.
- Perform calculations with complex numbers and vectors.
- Describe functions geometrically (graphs, level curves, and tangent planes).
- Set up and calculate simple plane and volume integrals.
- Use of Maple for mathematical calculations.
Competences to
- Follow mathematical language and argumentation within the course's subject areas.
- Apply mathematical theories and models that appear in continued studies.
About the course: Statistical models, probability theory, and data analysis in R.
Knowledge of
- Understanding the concept of distribution, probability functions, and densities.
- Marginal and joint distributions as well as mean and variance.
- Basic statistical concepts: Estimation, confidence intervals, and hypothesis testing.
- Linear regression and sample analysis.
Skills in
- Calculate probabilities (incl. conditional) using basic definitions and calculation rules.
- Perform calculations regarding marginal/joint distributions.
- Perform estimation, calculate confidence intervals, and perform hypothesis testing.
- Perform relevant statistical calculations in the R programming language.
Competences to
- Translate text-based problems and experiments into mathematical formulas.
- Set up simple statistical models (including linear regression and t-tests).
- Assess the relevance of the models and quantify uncertainties regarding the conclusions.
About the course: The foundation of computer science: Logic, discrete mathematics, algorithms, and data structures.
Knowledge of
- Basic mathematical method, logic, and elementary number theory.
- Sets, relations, and functions.
- Asymptotic time and space complexity (Big-O notation).
- Basic data structures: Lists, stacks, queues, and binary search trees.
- Graphs, trees, and related algorithms.
Skills in
- Formulate simple mathematical arguments and proofs.
- Identify relevant mathematical tools for solving computer science problems.
- Analyze combinatorial problems (counting arguments and algebra).
- Determine the runtime of algorithms using asymptotic notation.
- Analyze advantages and disadvantages of selected algorithms and data structures.
Competences to
- Independently solve problems within logic, algorithms, and data structures.
- Select correct methods and theories for problem-solving, including performing formal logical operations.
About the course: Data wrangling, visualization, and design of data science pipelines.
Knowledge of
- Model design and implementation: Basic concepts, structuring, and testing strategies.
- Data exploration and visualization: Exploratory analysis and key concepts.
Skills in
- Write scripts for collecting and processing data as well as loading structured text.
- Design a modular pipeline for data analysis of a specific problem.
- Design meaningful visualizations.
Competences to
- Understand key challenges in an effective data science workflow.
- Design and understand modular data science pipelines.
- Produce meaningful visualizations and document workflows, methods, and results.
About the course: Design, implementation, and administration of relational databases as well as system development.
Knowledge of
- Central technical database concepts such as relational model, data independence, and transactions.
- Entity-Relationship modeling (ER modeling) and relational data modeling, including transformations from ER to relational model.
- Queries in database languages, including relational calculus, relational algebra, and SQL.
- The theory behind database normalization, including functional dependencies, keys, and relational decompositions.
- ACID (atomicity, consistency, isolation, durability) properties and use of transactions.
- Indexing techniques and their role in database query optimization.
- Use of constraints and triggers.
- Methods for reading structured text (e.g., regular expressions, finite automata, context-free grammars).
- Data protection regulation (GDPR).
Skills in
- Develop a data model and realize database applications – starting from ER modeling, via relational modeling and normalization, to a concrete SQL-based application.
- Plan and manage an agile, iterative, and learning-oriented system development process under given resource and time constraints.
Competences to
- Develop a database design and implement database applications.
- Participate effectively in an agile software development process as part of a development team.
About the course: Linear algebra with a focus on solving equations, matrices, and applications in computer science.
Knowledge of
- Fundamental topics: Solving equations, Gaussian elimination, and matrix calculus.
- Vector space theory: Bases for vector spaces, orthogonality, and determinants.
- Advanced topics: Eigenvalues, complex numbers, and diagonalization.
- Application possibilities in computer science and implementation of algorithms in F# or Python.
Skills in
- Master fundamental methods and algorithms in linear algebra such as matrix manipulation (incl. inversion), Gaussian elimination, and determining determinants.
- Determination of eigenvalues and eigenvectors – both manually and via computer-assisted calculations.
- Use complex numbers in calculations.
- Write mathematics and prepare projects in LaTeX.
Competences to
- Identify and solve general linear problems using matrices.
- Interpret the results of the fundamental methods and algorithms.
- Construct bases (including orthogonal) and determine dimension.
- Determine diagonalizability and perform change of basis.
About the course: The theory behind and application of supervised and unsupervised learning algorithms.
Knowledge of
- The fundamental principles of machine learning.
- Basic probability theory for modeling and analyzing data.
- The theoretical concepts behind classification, regression, and clustering.
- The mathematical foundation for selected machine learning algorithms.
- Basic assumptions behind the algorithms, their implications, and common pitfalls.
Skills in
- Prove generalization bounds based on validation errors and for countable hypothesis classes.
- Apply linear and non-linear techniques for classification and regression.
- Perform elementary dimensionality reduction and data clustering.
- Implement selected machine learning algorithms and use software libraries for problem-solving.
- Visualize and evaluate results obtained with machine learning techniques.
- Identify and handle common pitfalls in machine learning.
Competences to
- Recognize and describe potential applications of machine learning.
- Formalize and analyze machine learning problems rigorously.
- Compare, assess, and select machine learning methods for specific tasks.
- Solve real-world data mining and pattern recognition problems using machine learning techniques.
About the course: In-depth mathematical analysis of functions, series, and multi-dimensional spaces.
Knowledge of
- Know convergence criteria for sequences and series of numbers.
- Know basic concepts such as continuity, differentiability, and integrability, relating to functions of one or multiple variables.
- Know convergence concepts and criteria for sequences and series of functions, including power series and Fourier series.
Skills in
- Handle the limit concept of mathematical analysis with technical proficiency.
- Perform mathematical analysis of functions in one variable (investigate continuity, differentiability, integrability, and extrema).
- Perform mathematical analysis of functions from multiple variables to multiple variables, especially extrema investigation and optimization.
Competences to
- Determine the correctness and relevance of mathematical arguments within analysis.
- Argue with mathematical rigor in definitions and proofs.
- Analyze problems from multi-dimensional mathematical analysis, including assessing the relevance of differential and integral calculus in specific contexts.
About the course: Advanced neural networks, architectures, and training methods for complex data analysis.
Knowledge of
- Convolutional neural networks (CNNs).
- Transformers and their application.
- Message passing and graph neural networks.
- Generative neural networks such as variational autoencoders (VAEs).
- Basic strategies for interpretability of deep neural networks.
- Training methodology for deep models.
Skills in
- Select appropriate methodology to solve deep learning problems.
- Implement selected deep learning algorithms.
- Design and train own deep learning algorithms.
Competences to
- Reflect on the possibilities and limitations of deep learning algorithms.
- Recognize and describe potential applications of deep learning methodology.
- Design, optimize, and use deep models.
- Apply the learned methodology to the analysis of real-world data such as images, audio, and text.
- Analyze deep learning algorithms.
About the course: Parallelization, system programming, and hardware architecture.
Knowledge of
- Number representations, arithmetic, and boolean algebra.
- Instruction sets, machine language, processor architecture, and memory hierarchies.
- Threads, scheduling, and synchronization.
- Processes and virtual memory.
- Encoding of data in files and data networks.
- Parallel architectures.
Skills in
- Implement simple programs in a system programming language with explicit memory management.
- Explain motivations for concurrency, memory hierarchies, and virtual memory.
- Use standard tools for developing, modifying, and extending programs at the system level.
- Systematically test, debug, and measure the performance of system-level software.
- Implement simple programs on a parallel platform.
Competences to
- Reason about processor architecture, memory hierarchies, operating systems, and data networks.
- Analyze the performance of programs based on knowledge of the system's structure.
- Implement simple programs in a system programming language and on a parallel platform.
- Reason about the correctness of simple multi-threaded programs.
About the course: Modeling with Bayesian networks, graphical models, and probability algorithms.
Knowledge of
- Graphical representations of dependence and conditional independence.
- Standard probability propagation algorithms in a network.
- Standard examples of Bayesian networks.
- Gaussian models.
Skills in
- Master graph terminology as well as the relationship between graphs and probability models.
- Determine conditional independence using d-separation.
- Implement simulations of variables from a Bayesian network.
- Perform calculations with linear Gaussian networks (based on linear algebra) and discrete networks.
- Implement common probability propagation algorithms within the framework of Bayesian networks.
- Implement selected learning algorithms and apply them.
Competences to
- Determine correctness and relevance of algorithms as well as theoretical calculations within Bayesian networks.
- Assess whether a Bayesian network correctly represents a specific application.
- Evaluate and discuss advantages and disadvantages of an algorithm for a specific Bayesian network (e.g., in relation to runtime complexity or generality).
- Solve a major assignment that includes theoretical as well as practical elements, in collaboration with others.
About the course: Sorting, graph algorithms, dynamic programming, and complexity analysis.
Knowledge of
- Sorting algorithms.
- Algorithms for solving optimization problems in graphs.
- Priority queues and balanced search trees.
- Amortized analysis.
- Recursive algorithms and recurrence equations.
- Greedy algorithms.
- Dynamic programming.
- Computational geometry and parallel algorithms.
Skills in
- Recognize algorithmic paradigms such as recursion, dynamic programming, and greedy algorithms.
- Perform asymptotic complexity analysis of algorithms and data structures (including solving recurrence equations).
- Argue for the correctness of algorithms and data structures using induction (including the formulation of loop invariants) as well as direct and contradiction proofs.
Competences to
- Apply appropriate algorithms and data structures to new problems.
- Apply algorithmic paradigms to new problems.
About the course: Relevant combinatorial probability theory and randomized techniques for data analysis.
Knowledge of
- Relevant combinatorial probability theory and randomized techniques in algorithmics.
- Variance and standard deviation.
- Tail inequalities.
- Randomized data structures and randomized algorithms.
- Analysis of large data streams.
Skills in
- Show bounds for the expected runtime of randomized algorithms.
- Explain methods for bounding the probability that a random variable deviates far from its expected value.
Competences to
- Reason about and apply randomized techniques to data analysis problems.
- Find simple and efficient randomized algorithms and data structures where traditional deterministic methods are more difficult or less efficient.
About the course: Philosophy of science, ethics, and the role of computer science in society.
Knowledge of
- Philosophical, ethical, political, and legal discussions of both a general and subject-specific nature.
- The position of computer science relative to other disciplines.
- Various scientific methods.
Skills in
- Nuance an academic issue by selecting relevant viewpoints across different contexts.
- Prepare a written academic product, including correct referencing and independent selection of relevant syllabus.
Competences to
- Critically assess the scope of scientific methods and the relationship between computer science and the surrounding society.
- Reflect on scientific knowledge production (from basic research to innovation) as well as the epistemological status of computer science.
- Take an independent stance on the practitioner's and researcher's ethical responsibility and integrity.
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High School Education
STX - Kolding Gymnasium
Kolding | 2017 - 2020
Study Program: Math/Social Sciences - Math A and Social Sciences A.
A Level
- Mathematics
- Social Sciences
- History
- Danish
B Level
- English
- Physics
- Physical Education
- German
- Chemistry
C Level
- Visual Arts
- Classical Studies
- Religion
- Biology
- Rhetoric