Irena Swanson's written or co-edited books and lecture notes

Books

• Introduction to Analysis with Complex Numbers, 456 pages, published by World Scientific Publishing, 2021. This is a self-contained book that covers the standard topics in introductory analysis and that in addition constructs the natural, rational, real and complex numbers, and also handles complex-valued functions, sequences, and series. The book teaches how to write proofs. Fundamental proof-writing logic is covered in Chapter 1 and is repeated and enhanced in two appendices. Many examples of proofs appear with words in a different font for what should be going on in the proof writer's head. The book contains many examples and exercises to solidify the understanding. The material is presented rigorously with proofs and with many worked-out examples. Exercises are varied, many involve proofs, and some provide additional learning materials. Errata.
  
  
• Co-wrote Integral Closure of Ideals, Rings, and Modules, with Craig Huneke, published by Cambridge University Press, Cambridge, 2006. This is a graduate-level textbook, and it is also meant to be a reference for researchers.
  Click here to link to the book information at Cambridge University Press, and click here for chapter titles, errata, and the online version.
  
  
• Co-edited a collection of expository papers: Commutative Algebra, coedited with Marco Fontana, Salah-Eddine Kabbaj, and Bruce Olberding, published by Springer, 2011.
  Click here to link to the book information at Springer. Contributors: D. D. Anderson; D. F. Anderson, M. C. Axtell, J. A. Sticklers, Jr.; S. Bazzoni, S.-E. Kabbaj; H. Brenner; L. W. Christensen, H.-B. Foxby, H. Holm; M. Fontana, M. Zafrullah, H. Haghighi, M. Tousi, S. Yassemi; F. Halter-Koch; W. Heinzer, L. J. Ratliff, Jr., D. E. Rush; F.-V. Kuhlmann; K. A. Loper; B. Olberding; L. Salce; H. Schoutens; I. Swanson; M. Vitulli.
  
  
• Co-edited: Commutative Algebra and its Applications, coedited with Marco Fontana, Salah-Eddine Kabbaj, and Bruce Olberding, published by de Gruyter, 2009. Contributors: D. D. Anderson, M. Zafrullah; D. F. Anderson, A. Badawi, D. E. Dobbs, J. Shapiro; A. Badawi; C. Bakkari, N. Mahdou; V. Barucci; D. Bennis, N. Mahdou; S. Bouchiba; S. Bouchiba, S. Kabbaj; P. Cesarz, S. T. Chapman, S. McAdam, G. J. Schaeffer; J.-L. Chabert; F. Couchot; M. D'Anna, C. A. Finocchiaro, M. Fontana; D. E. Dobbs; D. E. Dobbs, G. Picavet; S. El Baghdadi; L. El Fadil; J. Elliott; Y. Fares; F. Halter-Koch; S. Hizem; A. Jhilal, N. Mahdou; S. Kabbaj, A. Mimouni; N. Mahdou, K. Ouarghi; R. Matsuda; S. B. Mulay; B. Olberding; L. Salce; S. Sather-Wagstaff; I. Swanson.
  Click here to link to the book information at de Gruyter.
  
  
• Ten lectures on tight closure, IPM Lecture Note Series, 3, Tehran, 2002. 93 pages. These are the notes from the mini course I gave at IPM (Institute for Studies in Theoretical Physics and Mathematics) in Tehran, Iran, in January 2002. It consists of approximately 65 pages of lectures and 5 pages of tight closure references. The latest version was posted on 7 July 2004: improvements were suggested by Janet Striuli and Graham Leuschke. I also changed spacing so more gets printed per page now. The sections are: 1. The basics; 2. Briancon-Skoda theorem, rings of invariants, ...; 3. The localization problem; 4. Tight closure for modules; 5. Application to symbolic and ordinary powers of ideals; 6. Test elements and the persistence of tight closure; 7. More on test elements, or what is needed in Section 5; 8. Tight closure in characteristic 0; 9. A bit on the Hilbert-Kunz function; 10. Summary of research in tight closure.
  
  

  Lecture notes

• (Unpublished) Summer Graduate Workshop at MSRI, Berkeley, 6 June-17 June 2011 Co-organizing and lecturing with Daniel Erman then from Stanford University, and Amelia Taylor, then from from Colorado College. The workshop will involve a combination of theory and symbolic computation in commutative algebra. The lectures are intended to introduce three active areas of research: Boij-Soederberg theory, algebraic statistics, and integral closure. The lectures will be accompanied with tutorials on the computer algebra system Macaulay 2. My first introductory lecture was on resolutions and I got to the proof of the Hilbert's Syzygy Theorem (at least of the graded modules). You can get here the slide version of the resolutions talk. My lectures two and three were on the Eisenbud-Sturmfels paper on binomial ideals. You can get here my notes on binomial ideals (updated in June 2013, in Valladolid, Spain). I did not present lattices and characters neither in my lectures nor in these notes; I think the omission made the lectures more easily understable to beginners.
  
  
• (Unpublished) Reed College, Spring 2011, MATH 411 Topics in Advanced Analysis: Functional Analysis. Banach, Hilbert spaces; compact, Fredholm, self-adjoint operators; spectral theory; Lp spaces. I am an algebraist, but I love (teaching) analysis. These pdf lecture notes are work in progress. Many examples are worked out, including counterexamples to the conclusions of big theorems if various hypotheses are removed. Feedback appreciated.
  
  
• My lecture notes for the School on Local Rings and Local Study of Algebraic Varieties, ICTP, Trieste 31 May-4 June 2010 in pdf format: Integral closure of ideals and rings (pdf). This school and conference was in honor of Tito Valla, and click here (pdf) for the song/poem in his honor that we sang at the end of my last talk. Here is Gemma Colome's recording of it. To hear what the singing could have been like, click here(mp3). The whistling accompaniment is by Adam Boocher.
  
  
• (Unpublished) My lecture notes on homological algebra (pdf), delivered at University of Rome III in March-May 2010, with significant improvements for lectures at University of Graz in the Winter Semester 2018, and more additions and corrections since.
  
  
• (Unpublished) Reed College, Spring 2009, MATH 332 Abstract Algebra: An elementary treatment of the algebraic structures of groups, rings, fields, and/or algebras. (These pdf lecture notes are work in progress. Feedback appreciated. In class I scatter some non-standard topics only on Tuesdays, but in the pdf notes they are all in one place.)