Using MixEmergency with Scratch Live, Serato DJ, or Serato DJ Pro you can mix and record your Video DJ sets from your mixer and turntables, or DJ controller.
To illustrate the depth of the book, let’s examine a representative exercise and its solution strategy (fully paraphrased, not reproduced).
Problem (Paraphrased):
Prove that the series
[
\sum_n=1^\infty\frac(-1)^n+1n
]
converges, and determine whether it converges absolutely.
Solution Sketch (Key Steps):
Pedagogical point: The problem forces the student to recognise the role of sign alternation and differentiate between conditional and absolute convergence—a concept that recurs throughout higher analysis.
Because the book is out of print, used copies are abundant and cheap.
| Part | Chapter(s) | Main Themes | |------|------------|-------------| | I. Foundations | 1. Logic & Proof, 2. Set Theory, 3. Functions & Relations | Formal logical language, propositional and predicate logic, methods of proof (direct, contrapositive, contradiction, induction), basic set operations, cardinalities, mappings. | | II. Number Theory | 4. Integers, 5. Divisibility, 6. Congruences, 7. Prime Numbers | Euclidean algorithm, Bézout’s identity, fundamental theorem of arithmetic, modular arithmetic, Chinese remainder theorem, Fermat’s little theorem, Euler’s theorem. | | III. Algebra | 8. Groups, 9. Rings, 10. Fields, 11. Polynomials | Definitions and examples, substructures, homomorphisms, Lagrange’s theorem, cyclic groups, isomorphism theorems, integral domains, factorisation, field extensions. | | IV. Linear Algebra | 12. Vector Spaces, 13. Linear Transformations, 14. Matrices | Basis, dimension, linear independence, rank–nullity theorem, eigenvalues/eigenvectors, diagonalisation, inner product spaces. | | V. Real Analysis | 15. Real Numbers, 16. Sequences & Series, 17. Continuity, 18. Differentiation, 19. Integration | Completeness of ℝ, limits, Cauchy sequences, power series, epsilon‑delta definitions, mean value theorem, Riemann integral, fundamental theorem of calculus. | | VI. Further Topics | 20. Metric Spaces, 21. Topology (basic), 22. Complex Numbers | Metric definitions, open/closed sets, compactness, connectedness, complex arithmetic, Argand diagram, De Moivre’s theorem. | pure mathematics by jk backhouse pdf full
(Exact chapter titles may vary slightly between editions, but the overall structure is consistent.)
First published in the 1960s and revised throughout the 1980s (notably the 3rd and 4th editions), Pure Mathematics was written in an era when textbooks were expected to be rigorous, concise, and unforgiving of laziness. Unlike many modern glossy textbooks filled with color photos and sidebars, Backhouse is dense. It is black, white, and brilliant.
Summary
Strengths
Limitations
Who it’s best for
Alternatives to consider (more depth or exercises)
Quick verdict A solid, proof-oriented undergraduate introduction that teaches rigorous thinking well; pair it with problem-rich or more application-oriented texts if you need wider scope or harder problems.
If you want, I can:
Yes—arguably more so.
Modern students are tempted to type integration problems into Wolfram Alpha or ChatGPT. Backhouse resists this. The value of the JK Backhouse text is that it trains mathematical thinking, not button-pushing.
If you work through the full Backhouse textbook (all chapters, all exercises), you will emerge with:
ChatGPT cannot give you that. A PDF of Backhouse—studied seriously—can.
| Option | Description | Typical Cost | Access Tips | |--------|--------------|--------------|-------------| | University Library (Physical) | Most UK and Commonwealth university libraries hold a copy in their mathematics collection. | Free (if you have library access) | Use the library catalogue; request inter‑library loan if not on‑site. | | Institutional e‑Book Subscription | Many universities subscribe to Pearson eText platforms (e.g., Pearson eCollege). | Covered by institutional licence | Search the e‑resource portal; look for “Pure Mathematics – J. K. Backhouse”. | | WorldCat / OCLC | Global library catalogue that can point you to the nearest holding library worldwide. | Free | Visit https://www.worldcat.org, enter title, locate a library near you. | | Used Book Market | Sites like AbeBooks, eBay, or Alibris often have the 3rd edition in good condition. | $25‑$60 (USD) | Verify edition (3rd) and ISBN: ISBN‑10: 0582093222. | | Legal PDF through Publisher | Pearson occasionally offers a PDF purchase for out‑of‑print titles via its Pearson Shop. | $40‑$80 (USD) | Search “Backhouse Pure Mathematics PDF” on the Pearson website; beware of third‑party sellers. | | Open‑Access Alternatives | If you need similar pure‑mathematics coverage, consider open textbooks like “Calculus Volume 1” by OpenStax or “Algebra” by the University of Cambridge OpenCourseWare. | Free | Not a substitute, but useful for supplemental study. |
Tip: If you are a current student, ask your lecturer or department librarian about a course‑specific licence. Many departments have a limited number of downloadable PDFs for enrolled students. To illustrate the depth of the book, let’s
CPU Usage of MixEmergency vs. Competing Software*
An enormous amount of work has gone into optimising MixEmergency 3.
Optimising CPU, GPU, and Memory usage has made MixEmergency the best performing Video DJing software by far.
*Tests conducted using the most recent versions of all software during February 2015, using a 2012 MacBook Air mixing two Full HD videos.
MixEmergency can send and receive high definition video streams over your local network using NewTek's innovative NDI technology. You can mix video between computers, easily change between Video DJs, mix with 3 or more decks, send your mix to a VJ, or send your mix to professional video production software.
MixEmergency has a recording system that is second to none.
Our intelligent recording system places almost no additional strain on your computer and ensures that your recordings won't suffer from the usual stuttering or dropped frames that others do.
Record once, export as many times as you want - at quality levels high enough for film production and high-definition television broadcast.
MixEmergency's transitions and effects are some of the best in the business. Production-quality and designed to run in real-time. Each plug-in is carefully considered and constructed - with focus and attention to detail.
Quickly and easily add text, image, Quartz Composition, and live video camera overlays to your performance.
Quartz Composition overlays allow you to add anything from simple logo animations, to live Twitter updates for your venue.
MixEmergency supports GPU-Accelerated video playback of H.264* and Hap encoded video.
The Hap video codec is great for encoding short loops or samples for use in MixEmergency's Sample Player.
*GPU-acceleration of H.264 encoded video requires compatible hardware.
Want to take your visuals to the next level? MixEmergency's Syphon input and output make it easy to send and receive real-time video between a number of popular video processing applications, such as MadMapper, VDMX, CoGe, Modul8, and Resolume Avenue.
Save and recall presets for effects, transitions, overlays, and more.
All in real-time, and MIDI mappable!
MixEmergency's revolutionary FX Sequencer allows you to layer, animate, and sequence up to 8 effects at once.
Recall entire sequences, or trigger one-shot animations, at the press of a button.
Use MixEmergency's Mixer FX feature to map the High, Mid., Low, Filter, and FX controls of your mixer, or controller, to MixEmergency's video effects.
It's the effects you want, designed by you, for your mixing style. Don't settle for less!
Almost every list, button, knob, and slider in MixEmergency can be mapped to a MIDI controller - giving you hands-on access to the functions most important to you. It's flexible, powerful, and easy to set up with the built-in MIDI learn capability. In addition, MixEmergency's MIDI output enables you to provide feedback directly to your MIDI controller; so you can light your controller's LEDs and meters.
Our effects and transitions can take advantage of your track's Beatgrid - giving effects and transitions a stronger visual impact, and enabling you to create synced lighting effects with your video screens.
Video signal paths can be complex - and some introduce a significant amount of delay to your video. Our user-adjustable delay compensation, automatic inter-frame compensation, and Delay Helper tool, allow you to output your video how it was intended: perfectly in sync with your audio.
