[TeX Introduction]. This is a practical introduction to TeX that intends to prepare the reader for using TeX and LaTeX. The introduction is far from comprehensive, but the idea is to give the reader the necessary background to understand how to look up anything they don't understand.
[Documentation]. This is a package that can be used to format a thesis at Rutgers according to their style guide.
[The Package]. Installation just requires putting the file in the folder your LaTeX file is in.
[Sample Thesis]. This is a sample output of a thesis just to show the formatting. The TeX document used to create this is here: [Sample Thesis TeX File]
[Borel Equivalence Relations]. I took notes over the course of a semester for a set theory class with Simon Thomas as the instructor. In the class, he focused on Borel equivalence relations, and countable Borel equivalence relations in particular. We went over methods involving Baire category, measure theory, and Martin's measure; and reaching topics relating to Martin's conjecture, and Borel combinatorics.
[Link to the CMI 2019 webpage]. I took notes for some of the lectures at The Core Model Induction and Other Inner Model Theoretic Tools meetings. In particular, the lectures by Trevor Wilson on determinacy and scales, and the lectures by Sandra Müller on computing \(\mathrm{HOD}\). These and other notes from the meeting can be found at the linked webpage.
[Why \(\mathsf{CH}\) is False]. These are the notes for a pizza seminar talk aimed at non-set theorists. In essence, it presents some quick, odd consequences of the continuum hypothesis relevant to other fields. Mostly this just consists of some quick results from either combinatorics or descriptive set theory. Obviously set theorists have their own intuitions about the continuum hypothesis, but such ideas can not be meaningfully presented in such a short time.
[Model Theory Preparation]. These notes were written to prepare for my oral qualifying exam. They cover at least an overview of the topics in model theory from my syllabus. This includes a curt introduction to basic logic; simple quantifier elmination; the fundamentals of types; the basics of prime, saturated, and homogeneous models; and a proof of Morley's categoricity theorem, with a bit on Morley rank and degree. Originally, I planned on making notes for each of the sections on my syllabus, but ultimately the whole project took too much time.
[Differential Equations Recitation Notes] can also be found without solutions. These are notes written over the course of a semester for section of an undergraduate course in differential equations, and so are probably littered with small errors and arithmetic mistakes.
[Paradoxes in Set Theory]. This is an overview of some paradoxical results as well as a background of both some first order logic and set theory. The "paradoxes" are then resolved (at least in the sense of not being outright contradictions). In particular, it covers Skolem's paradox, the axiom of foundation, Gödel's completeness and incompleteness theorems, reflection and compactness, and how non \(\omega\)-standard models interact with these. In addition to these results, which are dismissed as paradoxes, are several actual paradoxes including Russell's paradox, the Burali–Forti paradox, and Cantor's paradox.
[Jónsson Algebras]. Here are some notes on some basic Jónsson algebra results from the context of algebra.
[TeX Introduction]. This is a practical introduction to TeX that intends to prepare the reader for using TeX and LaTeX. The introduction is far from comprehensive, but the idea is to give the reader the necessary background to understand how to look up anything they don't understand.
[Documentation]. This is a package that can be used to format a thesis at Rutgers according to their style guide.
[The Package]. Installation just requires putting the file in the folder your LaTeX file is in.
[Sample Thesis]. This is a sample output of a thesis just to show the formatting. The TeX document used to create this is here: [Sample Thesis TeX File]
[Borel Equivalence Relations]. I took notes over the course of a semester for a set theory class with Simon Thomas as the instructor. In the class, he focused on Borel equivalence relations, and countable Borel equivalence relations in particular. We went over methods involving Baire category, measure theory, and Martin's measure; and reaching topics relating to Martin's conjecture, and Borel combinatorics.
[Link to the CMI 2019 webpage]. I took notes for some of the lectures at The Core Model Induction and Other Inner Model Theoretic Tools meetings. In particular, the lectures by Trevor Wilson on determinacy and scales, and the lectures by Sandra Müller on computing \(\mathrm{HOD}\). These and other notes from the meeting can be found at the linked webpage.
[Why \(\mathsf{CH}\) is False]. These are the notes for a pizza seminar talk aimed at non-set theorists. In essence, it presents some quick, odd consequences of the continuum hypothesis relevant to other fields. Mostly this just consists of some quick results from either combinatorics or descriptive set theory. Obviously set theorists have their own intuitions about the continuum hypothesis, but such ideas can not be meaningfully presented in such a short time.
[Model Theory Preparation]. These notes were written to prepare for my oral qualifying exam. They cover at least an overview of the topics in model theory from my syllabus. This includes a curt introduction to basic logic; simple quantifier elmination; the fundamentals of types; the basics of prime, saturated, and homogeneous models; and a proof of Morley's categoricity theorem, with a bit on Morley rank and degree. Originally, I planned on making notes for each of the sections on my syllabus, but ultimately the whole project took too much time.
[Differential Equations Recitation Notes] can also be found without solutions. These are notes written over the course of a semester for section of an undergraduate course in differential equations, and so are probably littered with small errors and arithmetic mistakes.
[Paradoxes in Set Theory]. This is an overview of some paradoxical results as well as a background of both some first order logic and set theory. The "paradoxes" are then resolved (at least in the sense of not being outright contradictions). In particular, it covers Skolem's paradox, the axiom of foundation, Gödel's completeness and incompleteness theorems, reflection and compactness, and how non \(\omega\)-standard models interact with these. In addition to these results, which are dismissed as paradoxes, are several actual paradoxes including Russell's paradox, the Burali–Forti paradox, and Cantor's paradox.
[Jónsson Algebras]. Here are some notes on some basic Jónsson algebra results from the context of algebra.
[Documentation]. This is a package that can be used to format a thesis at Rutgers according to their style guide.
[The Package]. Installation just requires putting the file in the folder your LaTeX file is in.
[Sample Thesis]. This is a sample output of a thesis just to show the formatting. The TeX document used to create this is here: [Sample Thesis TeX File]
[Borel Equivalence Relations]. I took notes over the course of a semester for a set theory class with Simon Thomas as the instructor. In the class, he focused on Borel equivalence relations, and countable Borel equivalence relations in particular. We went over methods involving Baire category, measure theory, and Martin's measure; and reaching topics relating to Martin's conjecture, and Borel combinatorics.
[Link to the CMI 2019 webpage]. I took notes for some of the lectures at The Core Model Induction and Other Inner Model Theoretic Tools meetings. In particular, the lectures by Trevor Wilson on determinacy and scales, and the lectures by Sandra Müller on computing \(\mathrm{HOD}\). These and other notes from the meeting can be found at the linked webpage.
[Why \(\mathsf{CH}\) is False]. These are the notes for a pizza seminar talk aimed at non-set theorists. In essence, it presents some quick, odd consequences of the continuum hypothesis relevant to other fields. Mostly this just consists of some quick results from either combinatorics or descriptive set theory. Obviously set theorists have their own intuitions about the continuum hypothesis, but such ideas can not be meaningfully presented in such a short time.
[Model Theory Preparation]. These notes were written to prepare for my oral qualifying exam. They cover at least an overview of the topics in model theory from my syllabus. This includes a curt introduction to basic logic; simple quantifier elmination; the fundamentals of types; the basics of prime, saturated, and homogeneous models; and a proof of Morley's categoricity theorem, with a bit on Morley rank and degree. Originally, I planned on making notes for each of the sections on my syllabus, but ultimately the whole project took too much time.
[Differential Equations Recitation Notes] can also be found without solutions. These are notes written over the course of a semester for section of an undergraduate course in differential equations, and so are probably littered with small errors and arithmetic mistakes.
[Paradoxes in Set Theory]. This is an overview of some paradoxical results as well as a background of both some first order logic and set theory. The "paradoxes" are then resolved (at least in the sense of not being outright contradictions). In particular, it covers Skolem's paradox, the axiom of foundation, Gödel's completeness and incompleteness theorems, reflection and compactness, and how non \(\omega\)-standard models interact with these. In addition to these results, which are dismissed as paradoxes, are several actual paradoxes including Russell's paradox, the Burali–Forti paradox, and Cantor's paradox.
[Jónsson Algebras]. Here are some notes on some basic Jónsson algebra results from the context of algebra.
[Borel Equivalence Relations]. I took notes over the course of a semester for a set theory class with Simon Thomas as the instructor. In the class, he focused on Borel equivalence relations, and countable Borel equivalence relations in particular. We went over methods involving Baire category, measure theory, and Martin's measure; and reaching topics relating to Martin's conjecture, and Borel combinatorics.
[Link to the CMI 2019 webpage]. I took notes for some of the lectures at The Core Model Induction and Other Inner Model Theoretic Tools meetings. In particular, the lectures by Trevor Wilson on determinacy and scales, and the lectures by Sandra Müller on computing \(\mathrm{HOD}\). These and other notes from the meeting can be found at the linked webpage.
[Why \(\mathsf{CH}\) is False]. These are the notes for a pizza seminar talk aimed at non-set theorists. In essence, it presents some quick, odd consequences of the continuum hypothesis relevant to other fields. Mostly this just consists of some quick results from either combinatorics or descriptive set theory. Obviously set theorists have their own intuitions about the continuum hypothesis, but such ideas can not be meaningfully presented in such a short time.
[Model Theory Preparation]. These notes were written to prepare for my oral qualifying exam. They cover at least an overview of the topics in model theory from my syllabus. This includes a curt introduction to basic logic; simple quantifier elmination; the fundamentals of types; the basics of prime, saturated, and homogeneous models; and a proof of Morley's categoricity theorem, with a bit on Morley rank and degree. Originally, I planned on making notes for each of the sections on my syllabus, but ultimately the whole project took too much time.
[Differential Equations Recitation Notes] can also be found without solutions. These are notes written over the course of a semester for section of an undergraduate course in differential equations, and so are probably littered with small errors and arithmetic mistakes.
[Paradoxes in Set Theory]. This is an overview of some paradoxical results as well as a background of both some first order logic and set theory. The "paradoxes" are then resolved (at least in the sense of not being outright contradictions). In particular, it covers Skolem's paradox, the axiom of foundation, Gödel's completeness and incompleteness theorems, reflection and compactness, and how non \(\omega\)-standard models interact with these. In addition to these results, which are dismissed as paradoxes, are several actual paradoxes including Russell's paradox, the Burali–Forti paradox, and Cantor's paradox.
[Jónsson Algebras]. Here are some notes on some basic Jónsson algebra results from the context of algebra.
[Link to the CMI 2019 webpage]. I took notes for some of the lectures at The Core Model Induction and Other Inner Model Theoretic Tools meetings. In particular, the lectures by Trevor Wilson on determinacy and scales, and the lectures by Sandra Müller on computing \(\mathrm{HOD}\). These and other notes from the meeting can be found at the linked webpage.
[Why \(\mathsf{CH}\) is False]. These are the notes for a pizza seminar talk aimed at non-set theorists. In essence, it presents some quick, odd consequences of the continuum hypothesis relevant to other fields. Mostly this just consists of some quick results from either combinatorics or descriptive set theory. Obviously set theorists have their own intuitions about the continuum hypothesis, but such ideas can not be meaningfully presented in such a short time.
[Model Theory Preparation]. These notes were written to prepare for my oral qualifying exam. They cover at least an overview of the topics in model theory from my syllabus. This includes a curt introduction to basic logic; simple quantifier elmination; the fundamentals of types; the basics of prime, saturated, and homogeneous models; and a proof of Morley's categoricity theorem, with a bit on Morley rank and degree. Originally, I planned on making notes for each of the sections on my syllabus, but ultimately the whole project took too much time.
[Differential Equations Recitation Notes] can also be found without solutions. These are notes written over the course of a semester for section of an undergraduate course in differential equations, and so are probably littered with small errors and arithmetic mistakes.
[Paradoxes in Set Theory]. This is an overview of some paradoxical results as well as a background of both some first order logic and set theory. The "paradoxes" are then resolved (at least in the sense of not being outright contradictions). In particular, it covers Skolem's paradox, the axiom of foundation, Gödel's completeness and incompleteness theorems, reflection and compactness, and how non \(\omega\)-standard models interact with these. In addition to these results, which are dismissed as paradoxes, are several actual paradoxes including Russell's paradox, the Burali–Forti paradox, and Cantor's paradox.
[Jónsson Algebras]. Here are some notes on some basic Jónsson algebra results from the context of algebra.
[Why \(\mathsf{CH}\) is False]. These are the notes for a pizza seminar talk aimed at non-set theorists. In essence, it presents some quick, odd consequences of the continuum hypothesis relevant to other fields. Mostly this just consists of some quick results from either combinatorics or descriptive set theory. Obviously set theorists have their own intuitions about the continuum hypothesis, but such ideas can not be meaningfully presented in such a short time.
[Model Theory Preparation]. These notes were written to prepare for my oral qualifying exam. They cover at least an overview of the topics in model theory from my syllabus. This includes a curt introduction to basic logic; simple quantifier elmination; the fundamentals of types; the basics of prime, saturated, and homogeneous models; and a proof of Morley's categoricity theorem, with a bit on Morley rank and degree. Originally, I planned on making notes for each of the sections on my syllabus, but ultimately the whole project took too much time.
[Differential Equations Recitation Notes] can also be found without solutions. These are notes written over the course of a semester for section of an undergraduate course in differential equations, and so are probably littered with small errors and arithmetic mistakes.
[Paradoxes in Set Theory]. This is an overview of some paradoxical results as well as a background of both some first order logic and set theory. The "paradoxes" are then resolved (at least in the sense of not being outright contradictions). In particular, it covers Skolem's paradox, the axiom of foundation, Gödel's completeness and incompleteness theorems, reflection and compactness, and how non \(\omega\)-standard models interact with these. In addition to these results, which are dismissed as paradoxes, are several actual paradoxes including Russell's paradox, the Burali–Forti paradox, and Cantor's paradox.
[Jónsson Algebras]. Here are some notes on some basic Jónsson algebra results from the context of algebra.
[Model Theory Preparation]. These notes were written to prepare for my oral qualifying exam. They cover at least an overview of the topics in model theory from my syllabus. This includes a curt introduction to basic logic; simple quantifier elmination; the fundamentals of types; the basics of prime, saturated, and homogeneous models; and a proof of Morley's categoricity theorem, with a bit on Morley rank and degree. Originally, I planned on making notes for each of the sections on my syllabus, but ultimately the whole project took too much time.
[Differential Equations Recitation Notes] can also be found without solutions. These are notes written over the course of a semester for section of an undergraduate course in differential equations, and so are probably littered with small errors and arithmetic mistakes.
[Paradoxes in Set Theory]. This is an overview of some paradoxical results as well as a background of both some first order logic and set theory. The "paradoxes" are then resolved (at least in the sense of not being outright contradictions). In particular, it covers Skolem's paradox, the axiom of foundation, Gödel's completeness and incompleteness theorems, reflection and compactness, and how non \(\omega\)-standard models interact with these. In addition to these results, which are dismissed as paradoxes, are several actual paradoxes including Russell's paradox, the Burali–Forti paradox, and Cantor's paradox.
[Jónsson Algebras]. Here are some notes on some basic Jónsson algebra results from the context of algebra.
[Differential Equations Recitation Notes] can also be found without solutions. These are notes written over the course of a semester for section of an undergraduate course in differential equations, and so are probably littered with small errors and arithmetic mistakes.
[Paradoxes in Set Theory]. This is an overview of some paradoxical results as well as a background of both some first order logic and set theory. The "paradoxes" are then resolved (at least in the sense of not being outright contradictions). In particular, it covers Skolem's paradox, the axiom of foundation, Gödel's completeness and incompleteness theorems, reflection and compactness, and how non \(\omega\)-standard models interact with these. In addition to these results, which are dismissed as paradoxes, are several actual paradoxes including Russell's paradox, the Burali–Forti paradox, and Cantor's paradox.
[Jónsson Algebras]. Here are some notes on some basic Jónsson algebra results from the context of algebra.
[Paradoxes in Set Theory]. This is an overview of some paradoxical results as well as a background of both some first order logic and set theory. The "paradoxes" are then resolved (at least in the sense of not being outright contradictions). In particular, it covers Skolem's paradox, the axiom of foundation, Gödel's completeness and incompleteness theorems, reflection and compactness, and how non \(\omega\)-standard models interact with these. In addition to these results, which are dismissed as paradoxes, are several actual paradoxes including Russell's paradox, the Burali–Forti paradox, and Cantor's paradox.
[Jónsson Algebras]. Here are some notes on some basic Jónsson algebra results from the context of algebra.
[Jónsson Algebras]. Here are some notes on some basic Jónsson algebra results from the context of algebra.