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Foundations of Mathematics for Deep Learning
8.3087
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Beschreibung
This intensive block course is designed to bridge the gap between basic high-school mathematics and the advanced mathematical concepts essential for deep learning. It equips students with the foundational knowledge and skills required to excel in deep learning applications, including Natural Language Processing and Computer Vision. The course is tailored for students aiming to prepare for deep-learning-based courses at the institute, offering a comprehensive journey from fundamental mathematical principles to their practical application in deep learning models.
Course Content:
- Linear Algebra and Its Application to Data: The course begins with an exploration of linear algebra, focusing on its significance in understanding and manipulating data. Students will learn about vectors and matrices, mastering the art of working with these structures to perform various data operations.
- Multivariate Calculus for Data Fitting: Building upon the linear algebra foundation, the course delves into multivariate calculus to demonstrate how to optimize fitting functions for precise data modeling. Starting from introductory calculus concepts, the course employs matrices and vectors to facilitate a deep understanding of data fitting techniques.
- Operationalizing Concepts with Python: Transitioning from theory to practice, this segment emphasizes the application of learned concepts through Python programming. Students will engage in numerous exercises to solidify their understanding and gain hands-on experience in mathematical modeling.
- Implementing Neural Networks: The culmination of the course focuses on the construction and training of neural networks. By applying linear algebra and calculus, students will comprehend the mechanics of forward and backward passes within neural networks. The course includes a practical project where participants will implement a simple neural network and the backpropagation algorithm from scratch, applying it to a learning task.
- Coding Interview-Inspired Exercises for Research Scientists and Engineers: In addition to the core curriculum, this course includes exercises inspired by coding interviews for research scientists and research engineers in big tech companies. These exercises are designed to challenge students and prepare them for the types of problem-solving scenarios they might encounter in a professional setting, further enhancing their readiness for careers in deep learning research and engineering.
Requirements:
- A basic understanding of high-school mathematics.
- Familiarity with Python or another programming language, although all course materials and projects will utilize Python.
Outcome:
Upon completion, participants will not only grasp the mathematical theories underpinning deep learning but also gain practical skills in applying these concepts through programming. Additionally, they will be equipped with the problem-solving abilities needed to excel in technical interviews and research roles within the tech industry. This course ensures students are well-prepared and confident to tackle the challenges of deep-learning-based courses and projects.
Weitere Angaben
Ort: nicht angegeben
Zeiten: Termine am Montag, 16.09.2024 12:00 - 18:00, Dienstag, 17.09.2024 09:00 - 12:00, Dienstag, 17.09.2024 13:00 - 16:00, Mittwoch, 18.09.2024 09:00 - 12:00, Mittwoch, 18.09.2024 13:00 - 16:00, Donnerstag, 19.09.2024 09:00 - 12:00, Donnerstag, 19.09.2024 13:00 - 16:00, Freitag, 20.09.2024 09:00 - 12:00, Freitag, 20.09.2024 13:00 - 16:00, Montag, 23.09.2024 12:00 - 18:00, Dienstag, 24.09.2024 09:00 - 12:00, Dienstag, 24.09.2024 13:00 - 16:00, Mittwoch, 25.09.2024 09:00 - 12:00, Mittwoch, 25.09.2024 13:00 - 16:00, Donnerstag, 26.09.2024 09:00 - 12:00, Donnerstag, 26.09.2024 13:00 - 16:00, Freitag, 27.09.2024 09:00 - 12:00, Freitag, 27.09.2024 13:00 - 16:00
Erster Termin: Montag, 16.09.2024 12:00 - 18:00
Veranstaltungsart: Blockseminar (Offizielle Lehrveranstaltungen)
Studienbereiche
- Cognitive Science > Bachelor-Programm
- Cognitive Science > Master-Programm
- Human Sciences (e.g. Cognitive Science, Psychology)
Research Areas:
Algebraic geometry 14-XX
K-theory 19-XX
Algebraic topology 55-XX
Publications:
- Cellularity of hermitian K-theory and Witt-theory (with Markus Spitzweck and Paul Arne Østvær)
- On the η-inverted sphere. K-Theory-Proceedings of the International Colloquium
- Gigantic random simplicial complexes Link (with Jens Grygierek, Martina Juhnke-Kubitzke, Matthias Reitzner and Tim Römer)
- On very effective hermitian K-theory Link (with Alexey Ananyevskiy and Paul Arne Østvær)
- The first stable homotopy groups of motivic spheres DOI (with Markus Spitzweck and Paul Arne Østvær)
- Vanishing in stable motivic homotopy sheaves (with Kyle Ormsby and Paul Arne Østvær) Link
- The multiplicative structure on the graded slices of hermitian K-theory and Witt-theory (with Paul Arne Østvær) Link
- Slices of hermitian K–theory and Milnor's conjecture on quadratic forms (with Paul Arne Østvær) Link
- Calculus of functors and model categories, II (with Georg Biedermann) Link
- The Arone-Goodwillie spectral sequence for Σ∞Ωn and topological realization at odd primes (with Sebastian Buescher, Fabian Hebestreit und Manfred Stelzer) Link
- Motivic slices and coloured operads (with Javier Gutierrez, Markus Spitzweck and Paul Arne Østvær) Link
- Motivic strict ring models for K-theory (with Markus Spitzweck and Paul Arne Østvær) PDF
- Theta characteristics and stable homotopy types of curves DOI
- A universality theorem for Voevodsky's algebraic cobordism spectrum (with Ivan Panin and Konstantin Pimenov) Link
- On the relation of Voevodsky's algebraic cobordism to Quillen's K-theory DOI (with Ivan Panin and Konstantin Pimenov)
- On Voevodsky's algebraic K-theory spectrum BGL (with Ivan Panin and Konstantin Pimenov)
- Rigidity in motivic homotopy theory DOI (with Paul Arne Østvær)
- Calculus of functors and model categories DOI (with Georg Biedermann and Boris Chorny)
- Motivic Homotopy Theory Link (with B.I.Dundas, M.Levine, P.A.Østvær and V.Voevodsky)
- Motives and modules over motivic cohomology Link (with Paul Arne Østvær)
- Modules over motivic cohomology DOI (with Paul Arne Østvær)
- Enriched functors and stable homotopy theory Link (with Bjørn Ian Dundas and Paul Arne Østvær)
- Motivic functors Link (with Bjørn Ian Dundas and Paul Arne Østvær)
Preprints and Talks:
Projekte
- DFG-Sachbeihilfe "Algebraic bordism spectra: Computations, filtrations, applications" (DFG-RSF-Antrag mit Alexey Ananyevskiy)
- DFG-Sachbeihilfe "Applying motivic filtrations" (mit Marc Levine und Markus Spitzweck) im DFG Schwerpunktprogramm 1786
- DFG-Sachbeihilfe "Operads in algebraic geometry and their realizations" (mit Jens Hornbostel,
Markus Spitzweck und Manfred Stelzer) im DFG Schwerpunktprogramm 1786 - DFG Sachbeihilfe ``Operad structures in motivic homotopy theory'' im DFG Schwerpunktprogramm 1786 ``Homotopy theory and algebraic geometry'' (mit Markus Spitzweck)
- DFG Sachbeihilfe ``Motivic filtrations over Dedekind domains'' im DFG Schwerpunktprogramm 1786 ``Homotopy theory and algebraic geometry'' (mit Marc Levine und Markus Spitzweck)
- DFG Graduiertenkolleg 1916 ``Combinatorial structures in geometry''
- DFG Sachbeihilfe ``Goodwillie towers, realizations, and En-structures''
- Graduiertenkolleg ``Combinatorial structures in algebra and topology'' (mit H. Brenner, W. Bruns, T. Römer und R. Vogt)
- DFG Sachbeihilfe ``Combinatorial structures in algebra and topology'' (mit H. Brenner, W. Bruns, T. Römer und R. Vogt)
Supervision
PhD
Philip Herrmann: Stable equivariant motivic homotopy theory and motivic Borel cohomology, 2012
Florian Strunk: On motivic spherical bundles, 2013
Master/Diplom
Markus Severitt: Motivic Homotopy Types of Projective Curves, 2006 PDF
Philip Herrmann: Ein Modell für die motivische Homotopiekategorie, 2009
Florian Strunk: Ein Modell für motivische Kohomologie, 2009
Sebastian Büscher: Anwendung der F2-kohomologischen Goodwillie-Spektralsequenz für iterierte Schleifenraeume, 2010
Fabian Hebestreit: On topological realization at odd primes, 2010
Katharina Lorenz: Darstellung unterschiedlicher mathematischer Rekonstruktionen von Größen, 2012
Jana Brickwedde: Fehlvorstellungen zum Grenzwertbegriff, 2015
Lena-Christin Müller: Penrose-Parkettierungen und ihre Eigenschaften, 2015
Larissa Bauland: Der Satz von Seifert-van Kampen und einige seiner Anwendungen, 2018
Nikolaus Krause: Eine algebraische Einfuehrung in die Milnor-Witt K-Theorie, 2019
Bachelor
Ein Spezialfall des letzten Satzes von Fermat, 2010
Transzendente Zahlen, 2010
Zur Gruppe des Rubik-Wuerfels, 2011
Einige Betrachtungen zum letzten Satz von Fermat, 2012
Die Involution auf algebraischer K-Theorie, 2012
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Platonische und Archimedische Körper, 2012
Klassifikation regulärer Polyeder, 2013
Grundbegriffe der Trigonometrie und ihrer Umsetzung in der gymnasialen Sekundarstufe I, 2014
Die Riemann’sche Zetafunktion und der Primzahlsatz, 2014
Konstruktion der klassischen Zahlbereiche, 2014
Eigenschaften und spezielle Werte der Riemann'schen Zetafunktion, 2015
Das quadratische Reziprozitätsgesetz und dessen Bedeutung in der Kryptographie, 2015
Graphen färben, 2015
Klassifikation und Visualisierung von Koniken, 2016
Konstruktion von Polygonen mit einem einzigen Schnitt, 2016
Parkettierungen der Ebene durch kongruente konvexe Fuenfecke, 2019
Die klassischen Hopf-Faserbuendel und einige ihrer Eigenschaften, 2019
Einige Anmerkungen mathematischer und historischer Natur zu Fermats Letztem Satz, 2019