| Things to do in London this week for £5 or less. Hear about the mathematical side of Wren's work1. Swot up on British treasures The provenance of certain items in the British Museum is the subject of a fairly heated debate at the moment, but there's none of that at this free online talk which focuses on 10 of the museums artefacts which were discovered here in the UK. Guildhall Library hosts Dr William Sterling to discuss the artefacts, which were chosen by a panel of experts to mark the museum's 250th anniversary back in 2003. Some are predictable (hello, Sutton Hoo), but others might surprise you. Free, 7 March. 2. Attend a lunchtime concert in an art gallery Not just any art gallery — the National Gallery. Many venues offer lunchtime concerts these days, but the National Gallery's aren't all that well known. Head to Room 9 on Level 2 of the Trafalgar Square institution for a free performance by mezzo soprano Simone Jonetsu Ibbett-Brown and pianist JongSun Woo, members of the Black British Classical Foundation, which helps people of colour to participate in classical arts. The room is home to works by Michelangelo, Veronese and Titian, so it's a treat for the eyes as well as the ears. Free, 7 March 3. Wrangle with Wren's maths Sir Christopher Wren is often thought of as a creative type — no surprise when you admire the beauty of his magnum opus, St Paul's Cathedral. But he was also a mathematician (and Gresham Professor of Astronomy), and today's Gresham College lecture looks at the mathematical dimension of his work, including the calculations behind those spires and domes that we all love to admire. Sarah Hart, Professor of Geometry, gives the talk. It's part of the Wren 300 series, marking three centuries since his death. Free, 7 March. The St Patrick's Day parade is on Sunday. Image: iStock/Sebastien Mercier4. Be inspired by Peggy Guggenheim On International Women's Day, Guildhall Library celebrates American art collector Peggy Guggenheim, who championed artists from the Dada, Surrealist, and Abstract Expressionist movements, changing the face of 20th century art in the process. Arts Society lecturer Alexandra Epps gives a talk about Guggenheim's life, work and legacy — and you can watch it in person or online. Free, 8 March 5. Get your fill of gunpowder, treason and plot Visit the National Archives without leaving your living room. Image LondonVisited the National Archives' current exhibition, Treason: People, Power & Plot yet? See the highlights from home with a free online curator tour, telling the stories of traitors between the 1350s-1940s — some of whom changed British history — and whether they were convicted or acquitted. The event includes a short film, and a chance to ask the curators your questions. Free, 8 March. 6. Sweat it out at a HIIT class Over the next few weeks, athletics brand Asics offers several free classes and workouts from its Oxford Street store, mainly aimed at helping runners improve their performance. They include a HIIT class at the specially designed studio within the store, led by experienced runner, fitness coach and trainer Rey Smart. Free, 9 March (and other dates). 7. Visit a working windmill in Brixton Not many windmills remain in London — especially those making their own flour — but Brixton's is one of them, and this weekend it reopens for visiting season. On a 30-minute tour of the windmill, you'll learn how the machinery has been adapted to be run from wind, to steam, and now to electricity. It's a popular little attraction, so book ahead. £5, 11-12 March and various other weekends until October 8. St Patrick's Day Festival and Parade The St Patrick's Day parade is on Sunday. Image: iStock/Sebastien MercierGuinness season is almost upon us and the celebrations start early with London's St Patrick's Day Festival and Parade, taking place in the city centre on Sunday. Line the route between Hyde Park and Trafalgar Square to watch the procession full of floats, live bands, Irish dancers and other entertainers passing through the streets, then head to Trafalgar Square for a huge free festival. Wearing green is advised. Free, 12 March. 9. Bag cheap London Zoo tickets Some people can geat cheap entry to London Zoo. Image: Peter Trimming via creative commonsA reminder than until the end of March, anyone receiving Universal Credit, Pension Credit, Working Tax Credit, Child Tax Credit, Employment and Support Allowance, Income Support or Jobseeker's Allowance can get entry to London Zoo for just £3. The Community Access Scheme has been fairly popular, selling out some days, so book well in advance, and avoid weekends for your best chance of getting tickets. Other reduced price tickets are available to people with disabilities or additional needs, refugees, and those over 60 who are at risk of social isolation. Full details on the London Zoo website. £3, until end of March. 10. Delve into murder, mayhem and mystery Technically Elstree & Borehamwood Museum is just outside the limits of Greater London, but they do put on a terrific free exhibition, so to hell with the rules. Murder, Mayhem and Mystery takes you on a journey into the dark side of the area's past, with exhibits including a pistol once belonging to Dick Turpin, and a chance for kids to dress up as Bobbies in a police phone box. Free, until 26 August Looking for more free things to do in London? Here are 102 of em! We've also compiled this epic map of free stuff in London. | 