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Boot Camps 2024 & Tutoring

Enlist in one or both of our IN-PERSON Math Boot Camps! The UH Manoa Department of Mathematics will conduct intensive non-credit courses for students who want to review the algebra and trigonometry concepts needed to be successful in MATH 140X and calculus courses. Led by two department Graduate Assistants in each Boot Camp course, students will strengthen their math skills through short lectures, group work, and practice problems.

These courses are designed for students who want to bridge their high school and college math courses with a review, want to revisit math concepts prior to taking the math placement exam, or who have already taken the math placement exam but want to place higher on the exam* by reviewing concepts and taking the placement exam again.

There are two Camps, with both offered at no cost:
Boot Camp for College Algebra, for those who desire an algebra refresher, on August 5-8, 2024 from 10am – 3pm, including a lunch break. Lunch will not be provided, so please bring your own “brown bag” lunch. Room: KELLER HALL 302.
Boot Camp for Trigonometry, for those who seek to brush up on trigonometry, on August 12-15, 2024 from 10 am – 2:30 pm, including a lunch break. Lunch will not be provided, so please bring your own “brown bag” lunch. Room: KELLER HALL 302.

To Register for our Algebra Boot Camp, please complete our Algebra Boot Camp Google Form. To register for our Trigonometry Boot Camp, please complete our Trigonometry Boot Camp Google Form. University of Hawai`i email address is required to complete the Google Form(s). If you would like to register for both Boot Camps, you must complete both of the Google Forms. Registration REQUIRED to attend the Boot Camp(s). Registration Form(s) due Thursday, August 1, 2024 by 12 noon Hawaii Standard Time. We are limited to a maximum of 45 attendees per Boot Camp, so please be aware that the Algebra and Trigonometry Boot Camp 2024 Google Forms may close prior to the application deadline.

* To be allowed another attempt at taking the placement exam, you must attend each day of the Camp(s) in which you are registered.
For information on the concepts covered in the placement exam, please go to the MATH Placement Webpage.

To download a PDF flyer about the 2024 MATH Boot Camps, please click here:
MATH BOOT CAMPS 2024 FLYER

In addition:

Math tutoring is available at the Learning Emporium this summer for students enrolled in UH Manoa’s MATH 134 through MATH 243. More details can be found here:

https://natsci.manoa.hawaii.edu/learningemporium/

 

Qualifying exams in topology

The topology qualifying exam covers topics in algebraic topology.
Material
  1. Some point set topological concepts: basic definitions, compactness, separation axiom, connectedness/path-connectedness, retractions, contractibility, quotient topologies.
  2. Homotopy theory: CW complexes, homotopic maps, properties of homotopy in CW complexes, homotopy equivalence, homotopy extension.
  3. Some group theory: free groups, free products, universal properties, presentations of groups.
  4. Brief overview of basic category-theoretic definitions: categories, functors, natural transformations, examples.
  5. The fundamental group: a brief discussion of homotopy groups and their functoriality, long exact sequences of homotopy groups, definition of the fundamental groupoid and the fundamental group, calculation of the fundamental group of a circle, winding numbers, the van Kampen theorem together with examples of fundamental group calculations, K(π, 1) spaces and their properties.
  6. Covering spaces: basic definitions, lifting properties, deck group actions, the Galois correspondence between covers and subgroups of the fundamental group.
  7. Brief overview of (co)homological algebra: (co)chain complexes, (co)chain maps, exact sequences, (co)homology, long exact sequences induced by short exact sequences.
  8. Homology: cellular and singular homology and their equivalence, reduced homology, relative homology, excision, Mayer–Vietoris sequences, the Künneth formula, examples, first homology and the fundamental group, homology with coefficients, definition of cohomology and calculation of examples.
  9. Applications of homology: orientability, degrees of mappings, Lefschetz fixed point theorem, Brouwer fixed point theorem, invariance of domain Borsuk–Ulam theorem.
  10. Structures on cohomology rings: universal coefficients theorem for homology/cohomology, the cup and cap products, calculating cohomology rings, intersection numbers, duality theorems.
Textbooks
The following textbooks are recommended:
  • Bredon, Topology and geometry
  • Hatcher, Algebraic topology
  • Spanier, Algebraic topology
Sample Exams
 

Qualifying exams in analysis

The following syllabus for the Analysis Qualifying Exam is based on the following references:
  • Rudin’s Real and Complex Analysis 3rd edition
  • Folland’s Real Analysis: Modern Techniques and Applications 2nd edition.
Material
Abstract Integration and positive Borel measures
  • Rudin (Chapters 1 and 2), Folland (Chapter 1 and Sections 2.1, 2.2, 2.3, 2.5 and 2.6).
σ-algebras and Borel sets, measurable functions, simple functions, elementary properties of measures, integration of positive functions (including Lebesgue’s Monotone Convergence Theorem and Fatou’s Lemma), integration of complex functions (including Lebesgue’s Dominated Convergence Theorem), sets of measure zero and complete measures, Borel measures and their regularity properties, Lebesgue measure on finite-dimensional Euclidean spaces and linear transformations, continuity properties of measurable functions (including Lusin’s Theorem).  
L^p spaces
  • Rudin (Chapter 3), Folland (Section 6.1).
  Convex functions and Jensen’s inequality, Hölder’s inequality and Minkowski’s inequality, completeness of L^p spaces, approximation by continuous function.  
Modes of Convergence
  • Folland (Section 2.4).
Almost everywhere convergence, convergence in measure, convergence in L^p spaces, uniform convergence and Egorov’s theorem, the relations between modes of convergence.  
Differentiation
  • Rudin (Chapter 7), Folland (Sections 3.4 and 3.5).
  Maximal inequalities, Lebesgue points and Lebesgue’s differentation theorem, Lebesgue’s density theorem, absolutely continuous functions and the fundamental theorem of calculus.
Integration on Product Spaces
  • Rudin (Chapter 8), Folland (Section 2.5).
  Measurability on cartesian products, product measures, Tonelli’s theorem and Fubini’s theorem, completeness of product measures.  
Convolutions
  • Folland (Sections 8.1 and 8.2).
  Continuity of translation in the L^p norm, basic properties of convolution, derivatives of convolutions and approximate identities, density of smooth functions in L^p spaces.
Complex Measures
  • Rudin (Chapter 6), Folland (Sections 3.1, 3.2, 3.3 and 6.2).
  Total variation, absolute continuity of measures, the theorem of Lebesgue-Radon-Nikodym, bounded linear functionals on L^p spaces.  
Sample Exams
Diagram-CubeinSpace

Cubes in space

Four Maui High students, with guidance from University of Hawaiʻi professors, have created an experiment to measure how plastic degrades under ultraviolet light.

It was selected by the Cubes in Space program — a competitive, international opportunity for students to send their experiments on a high-altitude NASA balloon flight.

The carefully designed and highly researched experiments must each fit into a tiny 4 by 4 by 4-centimeter cube.

Monique Chyba and Yuriy Mileyko are among the professors working with the Maui students.

Full story from HPR

University of Hawaiʻi at Mānoa