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pnelson0502@yahoo.com
(505) 239 - 4173
This website contains a series of upper-level undergraduate math courses that are essential to the foundations and knowledge of applied mathematicians. Course numberings are based on the courses offered at UNM from when I was a student there. Some of these pages are an attempt to preserve the content, materials, structure, and resources of very good or exceptional courses (in my opinon). This website is for my purposes (reviewing and re-learning important concepts), but it is also a great source for self- or independent study. I have slightly modified all the courses' content, materials, structure, and resources based on my judgment of what needs emphasis in the curriculum. All professors will be given due credit - some of whom I had as instructors, some of whom I simply interacted with.
Math 264: Calculus III
Professor Nitsche, during my years as a college student, was the coordinator for the calculus sequence (Math 162: Calculus I, Math 163: Calculus II, and Math 264: Calculus III) for engineers at the University of New Mexico. She was my professor for Math 401 and deeply cares about teaching, holding students to high standards and expectations. As of Fall 2018, she was no longer the coordinator for the calculus sequence. I have kept and preserved all of her materials for Calculus III.
Math 311: Vector Analysis
I was one of the students in Dr. McConnell's section of Math 311 back in Fall 2018. The course was very well-organized and well-paced. The difficulty of the course was very fair. In particular, Professor McConnell omitted Calculus III concepts that were not essential to the central topics of the course: the integral theorems. As a result, the course met all of the objectives without being overly overwhelming in the breadth of the topics covered. His homework problems are now typed and posted. The organization and pacing of the course are based on his plans.
Math 312: Partial Differential Equations
Dr. Alexander Korotkevich, Fall 2017
I was one of the students in Dr. Alexander Korotkevich's 312 section back in Fall 2017. His course, though, was much more comprehensive and extensive. In my Math 312 course, I have cut down the amount of sections and topics covered (while ensuring that all of the major topics and objectives have been covered). New lecture notes were formulated (handwritten). All homework problems (from the sections that are covered) were selected by Professor Korotkevich (now typed).
Math 313: Complex Variables
Dr. Monika Nitsche, Spring 2016
I never had Professor Nitsche for Math 313, but was impressed by how well she organized her Math 313 course. Lectures and homework problems come from her. This particular course can easily become overly overwhelming if the course is not well-organized.
Math 316: Applied Ordinary Differential Equations
Dr. Mohammad Motamed, Spring 2017
I was one of the students in Dr. Mohammad Motamed's ODE section back in Spring 2017. All the materials posted (modified and generalized) come from Professor Motamed. However, he did not have time during that semester to cover an introduction to the Laplace Transform, which I have added to the lecture notes.
Math 321: Linear Algebra with Proofs
I was one of the students in Dr. Hongnian Huang's Linear Algebra section back in Fall 2016. The homework problems were selected by Professor Huang. He did not have time to cover inner product spaces, which I have decided to include in the list of topics.
Math 375: Introduction to Numerical Computing
Dr. Mohammad Motamed, Spring 2018
Dr. Motamed's Math 375 course was simply perfect- one of the best I took. The course was complete and well-developed. His homework assignments were relevant and meant to explore, in greater depth, what was discussed in class (using what was discussed in class). The class used MATLAB, but the course is not about MATLAB. It is about scientific computing (an introduction), and the MATLAB programming language was the language through which math and computer science majors explored the merits and errors of computers in computation in a wide range of different contexts in mathematics. All the course materials (slightly modified) come from him. There is no reason why his materials should not be preserved here.
Math 401: Advanced Calculus I
Professor Pereyra and Professor Nitsche are both the sources from which I drew material for the Advanced Calculus course. Professor Nitsche was my professor for the subject, and all of the homework problems for this course comes from her (with typos in the typed-up homework corrected). The pacing for the course also comes from her. Professor Pereyra was my faculty advisor in the math department, and it was professor Pereyra who regularly taught Math 401 with Terence Tao's Analysis I book. Steven Lay's book, used by Professor Nitsche, was a more "standard" or "traditional" approach to introductory analysis (with an introduction to proof). Lay's book proved friendlier to math students who were not previously familiar with writing proofs. Thus, I stayed with Steven Lay's book. However, the construction of the natural numbers, the integers, and the rational numbers are interesting topics worth exploring; thus, similar to Dr. Pereyra's Math 361 (the previous numbering for Math 401), I have included the construction of such number systems as a project. The modified Math 401 course (materials posted), then, are influenced my both Nitsche and Pereyra. It was my favorite math class back when I was a student.
Math 402: Advanced Calculus II
Dr. Maria Cristina Pereyra, Spring 2019
I never took this course when I was an undergraduate math student. Thus, part of the reason why it was important for me to preserve Dr. Pereyra's materials in this case was so that I could go back and study the subject myself. The materials come from Dr. Pereyra's 402 section in spring of 2019. The course is based on hers.
Other Courses of Interest:
Math 322: Modern Algebra
Prerequisites: Calculus III & Linear Algebra
Text: A First Course in Abstract Algebra, 7th Edition, by John B. Fraleigh
Supplementary Text: Undergraduate Algebra, 3rd Edition, by Serge Lang
I never took Math 322, so this is for my purposes (independent study). John Fraleigh's text is considered a classic one for the subject matter, and Dr. Vassilev made sure that students learned all the topics needed in an introductory abstract algebra course. I never knew Dr. Vassilev personally.
Math 441: Probability
Prerequisite: Calculus III
Text: Statistical Inference, 2nd Edition, by Casella and Berger
Supplementary Text: A First Course in Probability, 8th Edition, by Sheldon Ross
I was one of the students in Dr. Zhang's Probability class, a hybrid of both undergraduate and graduate students. It was a math elective for both math and statistics majors. The materials come from his course, although I have made slight modifications to the course structure.
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